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<b>let </b><font color="Maroon" title="c1">H</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">v</font> being <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><br/> for <font color="Olive" title="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="Olive" title="b2">v</font></span>)</span>  st <font color="Olive" title="b1">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Olive" title="b2">v</font> holds <br/>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="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Olive" title="b2">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b4">i</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> <font color="Maroon" title="c1">H</font> holds <br/> <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Olive" title="b1">w</font>,<font color="Olive" title="b2">v</font>,<font color="Olive" title="b3">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Olive" title="b2">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">v</font> being <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><br/> for <font color="Olive" title="b2">U</font> being   <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="orders_1.html#K1" title="ORDERS_1:func.1">BOOL</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Olive" title="b1">v</font></span>)</span>  st <font color="Maroon" title="c2">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Olive" title="b1">v</font> holds <br/>for <font color="Olive" title="b3">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Olive" title="b1">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Olive" title="b3">i</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> <font color="Maroon" title="c1">H</font> holds <br/> <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Olive" title="b1">v</font>,<font color="Olive" title="b2">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b3">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Olive" title="b1">v</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">v</font> be  <a href="modelc_3.html#V5" title="MODELC_3:attr.5">neg-inner-most</a> <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">U</font> being   <a href="orders_1.html#M1" title="ORDERS_1:mode.1">Choice_Function</a> of  <a href="orders_1.html#K1" title="ORDERS_1:func.1">BOOL</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c3">v</font></span>)</span>  st <font color="Maroon" title="c2">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c3">v</font> holds <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="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Olive" title="b1">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="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>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Olive" title="b2">i</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> <font color="Maroon" title="c1">H</font> holds <br/> <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Olive" title="b1">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="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>,<font color="Maroon" title="c3">v</font></span>)</span></span><br/><b>let </b><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="c3">v</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c3">v</font> implies 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="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Olive" title="b1">i</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> <font color="Maroon" title="c1">H</font> holds <br/> <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> )</span><br/>







<b>assume </b><a NAME="E1:157"/><i><font color="Green" title="E126">A0</font></i>: 
<font color="Maroon" title="c2">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c3">v</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">i</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Olive" title="b1">i</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> <font color="Maroon" title="c1">H</font> holds <br/> <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span><br/>

<a NAME="E2:157"/>
for <font color="Olive" title="b1">j</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Olive" title="b1">j</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> <font color="Maroon" title="c1">H</font> holds <br/> <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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> <font color="Maroon" title="c1">H</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> )</span><br/>

<b>set </b><font color="Maroon" title="c6">LN</font> =  <a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c3">v</font>;<br/>
<b>set </b><font color="Maroon" title="c7">s</font> =  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>;<br/>
<b>set </b><font color="Maroon" title="c8">s1</font> =  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>;<br/>
<b>set </b><font color="Maroon" title="c9">w0</font> =  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font>;<br/>
<b>set </b><font color="Maroon" title="c10">N</font> =  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</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"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c11">f</font> =  <a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>;<br/>
<b>set </b><font color="Maroon" title="c12">n</font> =  <a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c13">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p5">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>;<br/>
<a NAME="E1:157_1"/><i><font color="Green" title="E127">A000</font></i>: 
 <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</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"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> <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="c3">v</font>
 
<b>by </b><i><a class="ref" href="modelc_3.html#D30" target="_self" title="MODELC_3:def.30">defLTLNodes</a></i>;<br/>
<a NAME="E2:157_1"/><i><font color="Green" title="E128">A1</font></i>: 
 <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="#E1:157"><i><font color="Green" title="E126">A0</font></i></a>, <a class="ref" href="modelc_3.html#T73" target="_self" title="MODELC_3:th.73">thBA05</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:157_1_1_1"/>
(  not  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</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"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> 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> <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> 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="157_1_1_1_1"><b>suppose </b></a><a NAME="E1:157_1_1_1_1"/><i><font color="Green" title="E129">B1</font></i>: 
not  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</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"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> 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"> ( <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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> <font color="Maroon" title="c1">H</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:157_1_1_1_1"/><i><font color="Green" title="E130">C0</font></i>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p5">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_1"><b>proof </b></a><div class="add">

<span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
<b>by </b><i><a class="ref" href="modelc_3.html#D50" target="_self" title="MODELC_3:def.50">Defchosenrun</a></i>
<br/>.= 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p5">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D49" target="_self" title="MODELC_3:def.49">Defchosennext</a>, <a class="txt" href="#E2:157_1"><i><font color="Green" title="E128">A1</font></i></a>, <a class="txt" href="#E1:157_1_1_1_1"><i><font color="Green" title="E129">B1</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E2:157_1_1_1_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"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p5">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
 <b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</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>set </b><font color="Maroon" title="c14">n1</font> = <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/><a NAME="E3:157_1_1_1_1"/><i><font color="Green" title="E131">C3</font></i>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b> <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>  <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c3">v</font> =  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_2.html#K1" title="MODELC_2:func.1">CastNat</a> $1</span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>;<br/><a NAME="E4:157_1_1_1_1"/>
 ex <font color="Olive" title="b1">L</font> being  <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a> st <br/>(  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; ( for <font color="Olive" title="b2">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b2">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Olive" title="b1">L</font> holds <br/><font color="Olive" title="b1">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">k</font>) ) )
 <b>from </b><i><a class="ref" href="finseq_1.html#S2" title="FINSEQ_1:sch.2">FINSEQ_1:sch 2</a>();<br/></i><b>then consider </b><font color="Maroon" title="c15">L</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><b> such that </b><br/><a NAME="E6:157_1_1_1_1"/><i><font color="Green" title="E132">C4</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 <b>and </b><br/><a NAME="E7:157_1_1_1_1"/><i><font color="Green" title="E133">C5</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st <font color="Olive" title="b1">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c15">L</font> holds <br/><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>)
 ;<br/><a NAME="E8:157_1_1_1_1"/><i><font color="Green" title="E134">C601</font></i>: 
 <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c15">L</font>
 <b>by </b><i><a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E9:157_1_1_1_1"/><i><font color="Green" title="E135">C6</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 holds <br/><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c16">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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c16">k</font> &amp; <font color="Maroon" title="c16">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 implies <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> )</span><br/>

<b>assume </b><a NAME="E1:157_1_1_1_1_2"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c16">k</font> &amp; <font color="Maroon" title="c16">k</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span><br/>

<a NAME="E2:157_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c16">k</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T3" title="FINSEQ_1:th.3">FINSEQ_1:3</a></i>;<br/>
<a NAME="E3:157_1_1_1_1_2"/><b>then </b>
<font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_2.html#K1" title="MODELC_2:func.1">CastNat</a> <font color="Maroon" title="c16">k</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
 
<b>by </b><i><a class="txt" href="#E7:157_1_1_1_1"><i><font color="Green" title="E133">C5</font></i></a>, <a class="txt" href="#E8:157_1_1_1_1"><i><font color="Green" title="E134">C601</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:157_1_1_1_1_2"/>
<font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default"><font color="Maroon" title="c16">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
 <b>by </b><i><a class="ref" href="modelc_2.html#D1" title="MODELC_2:def.1">MODELC_2:def 1</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><i><font color="Green" title="E136">C800</font></i>: <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 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"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="#E3:157_1_1_1_1"><i><font color="Green" title="E131">C3</font></i></a>, <a class="txt" href="#E9:157_1_1_1_1"><i><font color="Green" title="E135">C6</font></i></a></i>
<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"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="modelc_2.html#D1" title="MODELC_2:def.1">MODELC_2:def 1</a></i>
<br/>.= 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K22" title="MODELC_3:func.22">LTLNodes</a> <font color="Maroon" title="c3">v</font></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="funct_7.html#T86" title="FUNCT_7:th.86">FUNCT_7:86</a></i>
<br/>.= 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="#E1:157_1"><i><font color="Green" title="E127">A000</font></i></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>
<br/>.= 
 <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</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"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>
;<br/><a NAME="E11:157_1_1_1_1"/><i><font color="Green" title="E137">C801</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 <b>by </b><i><a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><i><font color="Green" title="E138">C8</font></i>: <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font></span>)</span> = 
 <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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="#E9:157_1_1_1_1"><i><font color="Green" title="E135">C6</font></i></a>, <a class="txt" href="#E11:157_1_1_1_1"><i><font color="Green" title="E137">C801</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a></i>
<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"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p5">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="modelc_2.html#D1" title="MODELC_2:def.1">MODELC_2:def 1</a></i>
;<br/><a NAME="E13:157_1_1_1_1"/><i><font color="Green" title="E139">C8p</font></i>: 
for <font color="Olive" title="b1">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font> holds <br/> ex <font color="Olive" title="b2">N1</font>, <font color="Olive" title="b3">M1</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="c3">v</font> st <br/>( <font color="Olive" title="b2">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b3">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<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> &amp; <font color="Olive" title="b3">M1</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Olive" title="b2">N1</font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_5"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c16">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"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c16">k</font> &amp; <font color="Maroon" title="c16">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font> implies  ex <font color="Olive" title="b1">N1</font>, <font color="Olive" title="b2">M1</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="c3">v</font> st <br/>( <font color="Olive" title="b1">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> &amp; <font color="Olive" title="b2">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Olive" title="b2">M1</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Olive" title="b1">N1</font> ) )</span><br/>

<b>assume </b><a NAME="E1:157_1_1_1_1_5"/><i><font color="Green" title="E140">D1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c16">k</font> &amp; <font color="Maroon" title="c16">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">N1</font>, <font color="Olive" title="b2">M1</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="c3">v</font> st <br/>( <font color="Olive" title="b1">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> &amp; <font color="Olive" title="b2">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Olive" title="b2">M1</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Olive" title="b1">N1</font> )</span><br/>

<b>set </b><font color="Maroon" title="c17">k1</font> = <font color="Maroon" title="c16">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1;<br/>
<b>set </b><font color="Maroon" title="c18">kp</font> = <font color="Maroon" title="c16">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<a NAME="E2:157_1_1_1_1_5"/><i><font color="Green" title="E141">D200</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c16">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c16">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<b>by </b><i><a class="txt" href="#E1:157_1_1_1_1_5"><i><font color="Green" title="E140">D1</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c19">k1</font> = <font color="Maroon" title="c16">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="txt" href="#E1:157_1_1_1_1_5"><i><font color="Green" title="E140">D1</font></i></a>, <a class="ref" href="nat_1.html#T21" title="NAT_1:th.21">NAT_1:21</a></i>;<br/>
<a NAME="E4:157_1_1_1_1_5"/><i><font color="Green" title="E142">D2</font></i>: 
<font color="Maroon" title="c16">k</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
<b>by </b><i><a class="txt" href="#E1:157_1_1_1_1_5"><i><font color="Green" title="E140">D1</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a>, <a class="ref" href="xreal_1.html#T16" title="XREAL_1:th.16">XREAL_1:16</a></i>;<br/>
<b>set </b><font color="Maroon" title="c20">M1</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">k1</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> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>;<br/>
<b>set </b><font color="Maroon" title="c21">N1</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c19">k1</font></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>;<br/>
<a NAME="E5:157_1_1_1_1_5"/><i><font color="Green" title="E143">D3</font></i>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">k1</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> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c19">k1</font></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
 
<b>by </b><i><a class="txt" href="#E4:157_1_1_1_1_5"><i><font color="Green" title="E142">D2</font></i></a>, <a class="ref" href="modelc_3.html#D48" target="_self" title="MODELC_3:def.48">DefUsuccEndnum</a>, <a class="txt" href="#E2:157_1"><i><font color="Green" title="E128">A1</font></i></a>, <a class="txt" href="#E1:157_1_1_1_1"><i><font color="Green" title="E129">B1</font></i></a></i>;<br/>
<i><font color="Green" title="E144">D4</font></i>: <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <font color="Maroon" title="c19">k1</font></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="#E1:157_1_1_1_1_5"><i><font color="Green" title="E140">D1</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a>, <a class="txt" href="#E9:157_1_1_1_1"><i><font color="Green" title="E135">C6</font></i></a></i>
<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"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c19">k1</font></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="modelc_2.html#D1" title="MODELC_2:def.1">MODELC_2:def 1</a></i>
;<br/>
<font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
 <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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c16">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="#E2:157_1_1_1_1_5"><i><font color="Green" title="E141">D200</font></i></a>, <a class="txt" href="#E9:157_1_1_1_1"><i><font color="Green" title="E135">C6</font></i></a></i>
<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"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Maroon" title="c19">k1</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> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="modelc_2.html#D1" title="MODELC_2:def.1">MODELC_2:def 1</a></i>
;<br/>
<b>hence </b><a NAME="E8:157_1_1_1_1_5"/>
 ex <font color="Olive" title="b1">N1</font>, <font color="Olive" title="b2">M1</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="c3">v</font> st <br/>( <font color="Olive" title="b1">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">k</font> &amp; <font color="Olive" title="b2">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c16">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Olive" title="b2">M1</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Olive" title="b1">N1</font> )
 <b>by </b><i><a class="txt" href="#E5:157_1_1_1_1_5"><i><font color="Green" title="E143">D3</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1_5"><i><font color="Green" title="E144">D4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><a NAME="E14:157_1_1_1_1"/><b>then </b><i><font color="Green" title="E140">C9</font></i>: 
<font color="Maroon" title="c15">L</font> <a href="modelc_3.html#R5" title="MODELC_3:pred.5">is_Finseq_for</a> <font color="Maroon" title="c3">v</font>
 <b>by </b><i><a class="ref" href="modelc_3.html#D19" target="_self" title="MODELC_3:def.19">DefFinseq</a></i>;<br/><a NAME="E15:157_1_1_1_1"/><i><font color="Green" title="E141">C10</font></i>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p5">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>
 <b>by </b><i><a class="ref" href="modelc_3.html#D48" target="_self" title="MODELC_3:def.48">DefUsuccEndnum</a>, <a class="txt" href="#E2:157_1"><i><font color="Green" title="E128">A1</font></i></a>, <a class="txt" href="#E1:157_1_1_1_1"><i><font color="Green" title="E129">B1</font></i></a></i>;<br/><a NAME="E16:157_1_1_1_1"/>
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p5">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font> )
 <b>by </b><i><a class="txt" href="#E1:157"><i><font color="Green" title="E126">A0</font></i></a>, <a class="ref" href="modelc_3.html#T73" target="_self" title="MODELC_3:th.73">thBA05</a>, <a class="txt" href="#E2:157_1_1_1_1"><i><font color="Green" title="E130">C0</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a>, <a class="ref" href="nat_1.html#T11" title="NAT_1:th.11">NAT_1:11</a></i>;<br/><a NAME="E17:157_1_1_1_1"/><b>then </b><i><font color="Green" title="E142">C12</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a> 1
 <b>by </b><i><a class="txt" href="#E10:157_1_1_1_1"><i><font color="Green" title="E136">C800</font></i></a>, <a class="txt" href="#E1:157_1_1_1_1"><i><font color="Green" title="E129">B1</font></i></a>, <a class="txt" href="#E15:157_1_1_1_1"><i><font color="Green" title="E141">C10</font></i></a>, <a class="txt" href="#E12:157_1_1_1_1"><i><font color="Green" title="E138">C8</font></i></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></i>;<br/><a NAME="E18:157_1_1_1_1"/>
( <font color="Maroon" title="c1">H</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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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> <font color="Maroon" title="c1">H</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_6"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c16">H2</font> =  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font>;<br/>
<b>assume </b><a NAME="E1:157_1_1_1_1_6"/><i><font color="Green" title="E143">D1</font></i>: 
( <font color="Maroon" title="c1">H</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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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> <font color="Maroon" title="c1">H</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span><br/>

<a NAME="E2:157_1_1_1_1_6"/><i><font color="Green" title="E144">D3</font></i>: 
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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c3">v</font>
 
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a>, <a class="txt" href="#E10:157_1_1_1_1"><i><font color="Green" title="E136">C800</font></i></a></i>;<br/>
<a NAME="E3:157_1_1_1_1_6"/><i><font color="Green" title="E145">D4</font></i>: 
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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</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 <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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a>, <a class="txt" href="#E12:157_1_1_1_1"><i><font color="Green" title="E138">C8</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c17">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><b> such that </b><br/><a NAME="E5:157_1_1_1_1_6"/><i><font color="Green" title="E146">D501</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c17">m</font> &amp; <font color="Maroon" title="c17">m</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; not <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E14:157_1_1_1_1"><i><font color="Green" title="E140">C9</font></i></a>, <a class="txt" href="#E2:157_1_1_1_1_6"><i><font color="Green" title="E144">D3</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a>, <a class="txt" href="#E17:157_1_1_1_1"><i><font color="Green" title="E142">C12</font></i></a>, <a class="txt" href="#E3:157_1_1_1_1_6"><i><font color="Green" title="E145">D4</font></i></a>, <a class="txt" href="#E1:157_1_1_1_1_6"><i><font color="Green" title="E143">D1</font></i></a>, <a class="ref" href="modelc_3.html#T27" target="_self" title="MODELC_3:th.27">ThSucc03</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c18">N1</font>, <font color="Maroon" title="c19">N2</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="c3">v</font><b> such that </b><br/><a NAME="E7:157_1_1_1_1_6"/><i><font color="Green" title="E147">D5p</font></i>: 
( <font color="Maroon" title="c18">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">m</font> &amp; <font color="Maroon" title="c19">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c17">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> &amp; <font color="Maroon" title="c19">N2</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c18">N1</font> )
 <b>by </b><i><a class="txt" href="#E13:157_1_1_1_1"><i><font color="Green" title="E139">C8p</font></i></a>, <a class="txt" href="#E5:157_1_1_1_1_6"><i><font color="Green" title="E146">D501</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a></i>;<br/>
<a NAME="E8:157_1_1_1_1_6"/><i><font color="Green" title="E148">D5p1</font></i>: 
( <font color="Maroon" title="c18">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<font color="Maroon" title="c3">v</font> &amp; <font color="Maroon" title="c19">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c17">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> )
 
<b>by </b><i><a class="txt" href="#E7:157_1_1_1_1_6"><i><font color="Green" title="E147">D5p</font></i></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>;<br/>
<b>set </b><font color="Maroon" title="c20">mm1</font> = <font color="Maroon" title="c17">m</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1;<br/>
<b>reconsider </b><font color="Maroon" title="c21">mm1</font> = <font color="Maroon" title="c17">m</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 as   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> <b>by </b><i><a class="txt" href="#E5:157_1_1_1_1_6"><i><font color="Green" title="E146">D501</font></i></a>, <a class="ref" href="nat_1.html#T21" title="NAT_1:th.21">NAT_1:21</a></i>;<br/>
<a NAME="E10:157_1_1_1_1_6"/><i><font color="Green" title="E149">D601</font></i>: 
<font color="Maroon" title="c17">m</font> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
<b>by </b><i><a class="txt" href="#E5:157_1_1_1_1_6"><i><font color="Green" title="E146">D501</font></i></a>, <a class="ref" href="xreal_1.html#T16" title="XREAL_1:th.16">XREAL_1:16</a></i>;<br/>
<b>set </b><font color="Maroon" title="c22">Nm1</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c21">mm1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span>;<br/>
<a NAME="E11:157_1_1_1_1_6"/><i><font color="Green" title="E150">D6</font></i>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c21">mm1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span> <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="c3">v</font>
 
<b>by </b><i><a class="txt" href="#E1:157_1"><i><font color="Green" title="E127">A000</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="E151">D7</font></i>: <font color="Maroon" title="c18">N1</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <font color="Maroon" title="c21">mm1</font></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="#E9:157_1_1_1_1"><i><font color="Green" title="E135">C6</font></i></a>, <a class="txt" href="#E5:157_1_1_1_1_6"><i><font color="Green" title="E146">D501</font></i></a>, <a class="txt" href="#E7:157_1_1_1_1_6"><i><font color="Green" title="E147">D5p</font></i></a></i>
<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"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c21">mm1</font></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="modelc_2.html#D1" title="MODELC_2:def.1">MODELC_2:def 1</a></i>
;<br/>
<a NAME="E13:157_1_1_1_1_6"/><b>then </b><i><font color="Green" title="E152">D7p</font></i>: 
(  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font> &amp; not <font color="Maroon" title="c18">N1</font> is <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a> )
 
<b>by </b><i><a class="txt" href="#E10:157_1_1_1_1_6"><i><font color="Green" title="E149">D601</font></i></a>, <a class="ref" href="modelc_3.html#D48" target="_self" title="MODELC_3:def.48">DefUsuccEndnum</a>, <a class="txt" href="#E2:157_1"><i><font color="Green" title="E128">A1</font></i></a>, <a class="txt" href="#E1:157_1_1_1_1"><i><font color="Green" title="E129">B1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c23">m1</font> = <font color="Maroon" title="c17">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<a NAME="E14:157_1_1_1_1_6"/><i><font color="Green" title="E153">D801</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c17">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c17">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<b>by </b><i><a class="txt" href="#E5:157_1_1_1_1_6"><i><font color="Green" title="E146">D501</font></i></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/>
<i><font color="Green" title="E154">D8</font></i>: <font color="Maroon" title="c19">N2</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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_2.html#K1" title="MODELC_2:func.1">CastNat</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c17">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="#E9:157_1_1_1_1"><i><font color="Green" title="E135">C6</font></i></a>, <a class="txt" href="#E14:157_1_1_1_1_6"><i><font color="Green" title="E153">D801</font></i></a>, <a class="txt" href="#E7:157_1_1_1_1_6"><i><font color="Green" title="E147">D5p</font></i></a></i>
<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"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p3">(<span class="default"><font color="Maroon" title="c21">mm1</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> <span class="p2">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="modelc_2.html#D1" title="MODELC_2:def.1">MODELC_2:def 1</a></i>
<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"><span class="p3">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c21">mm1</font></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="funct_7.html#T73" title="FUNCT_7:th.73">FUNCT_7:73</a></i>
<br/>.= 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p3">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c21">mm1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="#E1:157_1"><i><font color="Green" title="E127">A000</font></i></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></i>
<br/>.= 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <span class="p2">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K26" title="MODELC_3:func.26">choice_succ_func</a> <span class="p0">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <font color="Maroon" title="c21">mm1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p5">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="txt" href="#E11:157_1_1_1_1_6"><i><font color="Green" title="E150">D6</font></i></a>, <a class="ref" href="modelc_3.html#D36" target="_self" title="MODELC_3:def.36">Defchoicesuccfunc</a></i>
<br/>.= 
 <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c18">N1</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a>, <a class="txt" href="#E12:157_1_1_1_1_6"><i><font color="Green" title="E151">D7</font></i></a></i>
;<br/>
<a NAME="E16:157_1_1_1_1_6"/><i><font color="Green" title="E155">D10</font></i>: 
<font color="Maroon" title="c19">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c18">N1</font>,<font color="Maroon" title="c1">H</font>
 
<b>by </b><i><a class="txt" href="#E5:157_1_1_1_1_6"><i><font color="Green" title="E146">D501</font></i></a>, <a class="txt" href="#E7:157_1_1_1_1_6"><i><font color="Green" title="E147">D5p</font></i></a>, <a class="txt" href="#E8:157_1_1_1_1_6"><i><font color="Green" title="E148">D5p1</font></i></a>, <a class="ref" href="modelc_3.html#T28" target="_self" title="MODELC_3:th.28">ThSucc04</a></i>;<br/>
<a NAME="E17:157_1_1_1_1_6"/><i><font color="Green" title="E156">D11</font></i>: 
 <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="c18">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_6_3"><b>proof </b></a><div class="add">

<b>set </b><font color="Maroon" title="c24">M0</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c18">N1</font>;<br/>
<b>set </b><font color="Maroon" title="c25">M1</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c18">N1</font>;<br/>
<b>set </b><font color="Maroon" title="c26">M2</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font>;<br/>
<a NAME="E1:157_1_1_1_1_6_3"/><i><font color="Green" title="E157">E1</font></i>: 
( not <font color="Maroon" title="c1">H</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 <font color="Maroon" title="c18">N1</font> &amp; <font color="Maroon" title="c1">H</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 <font color="Maroon" title="c19">N2</font> )
 
<b>by </b><i><a class="txt" href="#E5:157_1_1_1_1_6"><i><font color="Green" title="E146">D501</font></i></a>, <a class="txt" href="#E7:157_1_1_1_1_6"><i><font color="Green" title="E147">D5p</font></i></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>;<br/>
<b>set </b><font color="Maroon" title="c27">G</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="c18">N1</font>;<br/>
<a NAME="E2:157_1_1_1_1_6_3"/><i><font color="Green" title="E158">E401</font></i>: 
 <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="c18">N1</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="c18">N1</font>
 
<b>by </b><i><a class="txt" href="#E13:157_1_1_1_1_6"><i><font color="Green" title="E152">D7p</font></i></a>, <a class="ref" href="modelc_3.html#T58" target="_self" title="MODELC_3:th.58">Thchoice</a></i>;<br/>
<a NAME="E3:157_1_1_1_1_6_3"/><i><font color="Green" title="E159">E5</font></i>: 
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_6_3_1"><b>proof </b></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:157_1_1_1_1_6_3_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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span>,<font color="Maroon" title="c18">N1</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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span>,<font color="Maroon" title="c18">N1</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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span> ) ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1_1_1"><b>suppose </b></a><a NAME="E1:157_1_1_1_1_6_3_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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span>,<font color="Maroon" title="c18">N1</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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><div class="add"><a NAME="E2:157_1_1_1_1_6_3_1_1_1_1"/><b>then </b>
 <a href="modelc_3.html#K25" title="MODELC_3:func.25">chosen_succ</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c18">N1</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="c18">N1</font></span>)</span>,<font color="Maroon" title="c18">N1</font>
 <b>by </b><i><a class="ref" href="modelc_3.html#D35" target="_self" title="MODELC_3:def.35">Defchosensucc</a></i>;<br/><b>hence </b><a NAME="E3:157_1_1_1_1_6_3_1_1_1_1"/>
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="#E15:157_1_1_1_1_6"><i><font color="Green" title="E154">D8</font></i></a>, <a class="txt" href="#E2:157_1_1_1_1_6_3"><i><font color="Green" title="E158">E401</font></i></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def206</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="157_1_1_1_1_6_3_1_1_1_2"><b>suppose </b></a><a NAME="E1:157_1_1_1_1_6_3_1_1_1_2"/><i><font color="Green" title="E160">EA1</font></i>: 
( 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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span>,<font color="Maroon" title="c18">N1</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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><div class="add"><a NAME="E2:157_1_1_1_1_6_3_1_1_1_2"/><b>then </b><i><font color="Green" title="E161">EB1</font></i>: 
<font color="Maroon" title="c19">N2</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="c18">N1</font></span>)</span>,<font color="Maroon" title="c18">N1</font>
 <b>by </b><i><a class="ref" href="modelc_3.html#D35" target="_self" title="MODELC_3:def.35">Defchosensucc</a>, <a class="txt" href="#E15:157_1_1_1_1_6"><i><font color="Green" title="E154">D8</font></i></a></i>;<br/><b>set </b><font color="Maroon" title="c28">S1</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="c18">N1</font></span>)</span>,<font color="Maroon" title="c18">N1</font>;<br/><b>set </b><font color="Maroon" title="c29">G2</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="c18">N1</font></span>)</span>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:157_1_1_1_1_6_3_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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span> ) or  not  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span>,<font color="Maroon" title="c18">N1</font></span>)</span> )
 </span><b>by </b><i><a class="txt" href="#E1:157_1_1_1_1_6_3_1_1_1_2"><i><font color="Green" title="E160">EA1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:157_1_1_1_1_6_3_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="c18">N1</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:157_1_1_1_1_6_3_1_1_1_2_1_1_1"/>
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="#E2:157_1_1_1_1_6_3"><i><font color="Green" title="E158">E401</font></i></a>, <a class="txt" href="#E2:157_1_1_1_1_6_3_1_1_1_2"><i><font color="Green" title="E161">EB1</font></i></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def207</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="157_1_1_1_1_6_3_1_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:157_1_1_1_1_6_3_1_1_1_2_1_1_2"/><i><font color="Green" title="E162">EB4</font></i>: 
not  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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="c18">N1</font></span>)</span>,<font color="Maroon" title="c18">N1</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1_1_2_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1_1_2_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:157_1_1_1_1_6_3_1_1_1_2_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="c18">N1</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="c18">N1</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="c18">N1</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="c18">N1</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="c18">N1</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="c18">N1</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="c18">N1</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> )
 </span><b>by </b><i><a class="ref" href="modelc_2.html#T2" title="MODELC_2:th.2">MODELC_2:2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1_1_2_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:157_1_1_1_1_6_3_1_1_1_2_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="c18">N1</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="c18">N1</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="c18">N1</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="c18">N1</font> is <a href="modelc_2.html#V6" title="MODELC_2:attr.6">next</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:157_1_1_1_1_6_3_1_1_1_2_1_1_2_1_1_1"/>
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="#E13:157_1_1_1_1_6"><i><font color="Green" title="E152">D7p</font></i></a>, <a class="txt" href="#E2:157_1_1_1_1_6_3"><i><font color="Green" title="E158">E401</font></i></a>, <a class="txt" href="modelc_3.html#E38"><i><font color="Green" title="E29">LemSUM04</font></i></a>, <a class="txt" href="modelc_3.html#E39"><i><font color="Green" title="E30">LemSUM06</font></i></a>, <a class="txt" href="#E1:157_1_1_1_1_6_3_1_1_1_2_1_1_2"><i><font color="Green" title="E162">EB4</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_3_1_1_1_2_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:157_1_1_1_1_6_3_1_1_1_2_1_1_2_1_1_2"/>
(  <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="c18">N1</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="c18">N1</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="c18">N1</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/><div class="add"><b>hence </b><a NAME="E2:157_1_1_1_1_6_3_1_1_1_2_1_1_2_1_1_2"/>
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="txt" href="#E2:157_1_1_1_1_6_3"><i><font color="Green" title="E158">E401</font></i></a>, <a class="txt" href="#E2:157_1_1_1_1_6_3_1_1_1_2"><i><font color="Green" title="E161">EB1</font></i></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def207</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><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:157_1_1_1_1_6_3_1_1_1_2_1_1_2"/>
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E4:157_1_1_1_1_6_3_1_1_1_2"/>
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E2:157_1_1_1_1_6_3_1"/>
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></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>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_6_3_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:157_1_1_1_1_6_3_2"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <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="c18">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/><a NAME="E2:157_1_1_1_1_6_3_2"/><b>then </b>
not <font color="Maroon" title="c1">H</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_3.html#K24" title="MODELC_3:func.24">chosen_formula</a> <font color="Maroon" title="c4">U</font>,<font color="Maroon" title="c18">N1</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><b>hence </b><a NAME="E3:157_1_1_1_1_6_3_2"/>
contradiction
 <b>by </b><i><a class="txt" href="#E3:157_1_1_1_1_6_3"><i><font color="Green" title="E159">E5</font></i></a>, <a class="txt" href="#E1:157_1_1_1_1_6_3"><i><font color="Green" title="E157">E1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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="E5:157_1_1_1_1_6_3"/>
 <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="c18">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E18:157_1_1_1_1_6"/><i><font color="Green" title="E157">D12</font></i>: 
<font color="Maroon" title="c19">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c18">N1</font>
 
<b>by </b><i><a class="txt" href="#E17:157_1_1_1_1_6"><i><font color="Green" title="E156">D11</font></i></a>, <a class="txt" href="#E1:157_1_1_1_1_6"><i><font color="Green" title="E143">D1</font></i></a>, <a class="ref" href="modelc_3.html#D35" target="_self" title="MODELC_3:def.35">Defchosensucc</a>, <a class="txt" href="#E15:157_1_1_1_1_6"><i><font color="Green" title="E154">D8</font></i></a></i>;<br/>
<a NAME="E19:157_1_1_1_1_6"/><i><font color="Green" title="E158">D13</font></i>: 
( <font color="Maroon" title="c1">H</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="c18">N1</font> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> )
 
<b>by </b><i><a class="txt" href="#E1:157_1_1_1_1_6"><i><font color="Green" title="E143">D1</font></i></a>, <a class="txt" href="#E16:157_1_1_1_1_6"><i><font color="Green" title="E155">D10</font></i></a>, <a class="ref" href="modelc_3.html#D6" target="_self" title="MODELC_3:def.6">DefSucc01</a></i>;<br/>
<a NAME="E20:157_1_1_1_1_6"/>
 <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <font color="Maroon" title="c1">H</font> <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> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E1:157_1_1_1_1_6"><i><font color="Green" title="E143">D1</font></i></a>, <a class="ref" href="modelc_3.html#D2" target="_self" title="MODELC_3:def.2">Def204</a></i>;<br/>
<a NAME="E21:157_1_1_1_1_6"/><b>then </b><i><font color="Green" title="E159">D13p</font></i>: 
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c19">N2</font> <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="c18">N1</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"><font color="Maroon" title="c1">H</font></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> <font color="Maroon" title="c1">H</font></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="c18">N1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E18:157_1_1_1_1_6"><i><font color="Green" title="E157">D12</font></i></a>, <a class="txt" href="#E19:157_1_1_1_1_6"><i><font color="Green" title="E158">D13</font></i></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def207</a></i>;<br/>
<a NAME="E22:157_1_1_1_1_6"/><i><font color="Green" title="E160">D14</font></i>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">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> <span class="p4">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p4">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p5">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></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> <span class="p3">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
 
<b>by </b><i><a class="txt" href="#E12:157_1_1_1_1"><i><font color="Green" title="E138">C8</font></i></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>;<br/>
<a NAME="E23:157_1_1_1_1_6"/>
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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="#E15:157_1_1_1_1"><i><font color="Green" title="E141">C10</font></i></a>, <a class="ref" href="modelc_3.html#D11" target="_self" title="MODELC_3:def.11">Defelementary</a></i>;<br/>
<a NAME="E24:157_1_1_1_1_6"/><b>then </b>
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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c17">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</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 <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"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E22:157_1_1_1_1_6"><i><font color="Green" title="E160">D14</font></i></a>, <a class="txt" href="#E14:157_1_1_1_1"><i><font color="Green" title="E140">C9</font></i></a>, <a class="txt" href="#E14:157_1_1_1_1_6"><i><font color="Green" title="E153">D801</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a>, <a class="ref" href="modelc_3.html#T34" target="_self" title="MODELC_3:th.34">ThSucc10</a></i>;<br/>
<a NAME="E25:157_1_1_1_1_6"/><b>then </b><i><font color="Green" title="E161">D16</font></i>: 
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c19">N2</font> <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 <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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E7:157_1_1_1_1_6"><i><font color="Green" title="E147">D5p</font></i></a>, <a class="txt" href="#E22:157_1_1_1_1_6"><i><font color="Green" title="E160">D14</font></i></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>;<br/>
<a NAME="E26:157_1_1_1_1_6"/>
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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c17">m</font></span>)</span>,<font color="Maroon" title="c3">v</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 <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"><font color="Maroon" title="c15">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c15">L</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E5:157_1_1_1_1_6"><i><font color="Green" title="E146">D501</font></i></a>, <a class="txt" href="#E6:157_1_1_1_1"><i><font color="Green" title="E132">C4</font></i></a>, <a class="txt" href="#E14:157_1_1_1_1"><i><font color="Green" title="E140">C9</font></i></a>, <a class="ref" href="modelc_3.html#T31" target="_self" title="MODELC_3:th.31">ThSucc07</a></i>;<br/>
<a NAME="E27:157_1_1_1_1_6"/><b>then </b><i><font color="Green" title="E162">D17</font></i>: 
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c18">N1</font> <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 <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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E7:157_1_1_1_1_6"><i><font color="Green" title="E147">D5p</font></i></a>, <a class="txt" href="#E22:157_1_1_1_1_6"><i><font color="Green" title="E160">D14</font></i></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="157_1_1_1_1_6_4"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_4_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:157_1_1_1_1_6_4_1"/>
(  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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 <font color="Maroon" title="c18">N1</font> or  not  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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 <font color="Maroon" title="c18">N1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_4_1_1"><b>suppose </b></a><a NAME="E1:157_1_1_1_1_6_4_1_1"/>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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 <font color="Maroon" title="c18">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span><br/><div class="add"><b>hence </b><a NAME="E2:157_1_1_1_1_6_4_1_1"/>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E27:157_1_1_1_1_6"><i><font color="Green" title="E162">D17</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_1_6_4_1_2"><b>suppose </b></a><a NAME="E1:157_1_1_1_1_6_4_1_2"/><i><font color="Green" title="E163">D18</font></i>: 
not  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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 <font color="Maroon" title="c18">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span><br/><div class="add"><a NAME="E2:157_1_1_1_1_6_4_1_2"/>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:157_1_1_1_1_6_4_1_2"/><b>then </b>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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> <font color="Maroon" title="c1">H</font></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="c18">N1</font>
 <b>by </b><i><a class="txt" href="#E1:157_1_1_1_1_6_4_1_2"><i><font color="Green" title="E163">D18</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><a NAME="E4:157_1_1_1_1_6_4_1_2"/><b>then </b>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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="c19">N2</font>
 <b>by </b><i><a class="txt" href="#E21:157_1_1_1_1_6"><i><font color="Green" title="E159">D13p</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E5:157_1_1_1_1_6_4_1_2"/>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E25:157_1_1_1_1_6"><i><font color="Green" title="E161">D16</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></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E29:157_1_1_1_1_6"/>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#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> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="modelc_1.html#K31" title="MODELC_1:func.31">|**</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K35" title="MODELC_3:func.35">chosen_succ_end_num</a> <span class="p5">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p5">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p0">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p4">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span></span>)</span>,<font color="Maroon" title="c3">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="E19:157_1_1_1_1"/>
( <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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> <font color="Maroon" title="c1">H</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E2:157_1_1_1_1"><i><font color="Green" title="E130">C0</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="157_1_1_1_2"><b>suppose </b></a><a NAME="E1:157_1_1_1_2"/><i><font color="Green" title="E129">B2</font></i>: 
 <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</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"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> 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"> ( <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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> <font color="Maroon" title="c1">H</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:157_1_1_1_2"/><i><font color="Green" title="E130">C1</font></i>: 
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#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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#K9" title="MODELC_3:func.9">FinalNode</a> <font color="Maroon" title="c3">v</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E1:157_1_1_1_2"><i><font color="Green" title="E129">B2</font></i></a>, <a class="ref" href="modelc_3.html#D11" target="_self" title="MODELC_3:def.11">Defelementary</a></i>;<br/><a NAME="E3:157_1_1_1_2"/>
 <a href="modelc_3.html#K36" title="MODELC_3:func.36">chosen_next</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font>,<span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</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"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E2:157_1_1_1_2"><i><font color="Green" title="E130">C1</font></i></a>, <a class="txt" href="#E2:157_1"><i><font color="Green" title="E128">A1</font></i></a>, <a class="ref" href="modelc_3.html#D49" target="_self" title="MODELC_3:def.49">Defchosennext</a></i>;<br/><b>then </b> <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font> = 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <span class="p2">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>
<b>by </b><i><a class="ref" href="modelc_3.html#D50" target="_self" title="MODELC_3:def.50">Defchosenrun</a></i>
<br/>.= 
 <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</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"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span>
<b>by </b><i><a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">defCastNode01</a></i>
;<br/><b>hence </b><a NAME="E5:157_1_1_1_2"/>
( <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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> <font color="Maroon" title="c1">H</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">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></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:157_1"/>
( <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c5">j</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> <font color="Maroon" title="c1">H</font> implies  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c5">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">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="E3:157"/>
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="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font></span>)</span> &amp; <font color="Maroon" title="c1">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> &amp;  <a href="modelc_2.html#K32" title="MODELC_2:func.32">Shift</a> <font color="Maroon" title="c2">w</font>,<font color="Olive" title="b1">i</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> <font color="Maroon" title="c1">H</font> holds <br/> <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</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#K10" title="MODELC_3:func.10">CastNode</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="modelc_3.html#K37" title="MODELC_3:func.37">chosen_run</a> <font color="Maroon" title="c2">w</font>,<font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c4">U</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><font color="Olive" title="b1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span></span>)</span>,<font color="Maroon" title="c3">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>
