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<span class="kw">let </span><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">G</font>, <font color="Maroon" title="c3">v</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">s1</font>, <font color="Olive" title="b2">s0</font>, <font color="Olive" title="b3">s2</font> being   <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c3">v</font>  st <font color="Olive" title="b1">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b2">s0</font> &amp; <font color="Olive" title="b3">s2</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Olive" title="b1">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b1">s1</font> &amp;  not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b1">s1</font> holds <br/>( <font color="Maroon" title="c1">F</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="Olive" title="b1">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b3">s2</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">s1</font>, <font color="Maroon" title="c5">s0</font>, <font color="Maroon" title="c6">s2</font> be   <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#V3" title="MODELC_3:attr.3">elementary</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c3">v</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon" title="c5">s0</font> &amp; <font color="Maroon" title="c6">s2</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon" title="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> &amp;  not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> implies ( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> ) )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:97"/><span class="lab"><font color="Green" title="E86">A1</font></span>: 
<font color="Maroon" title="c4">s1</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon" title="c5">s0</font>
 <span class="kw">and </span><br/><a NAME="E2:97"/><span class="lab"><font color="Green" title="E87">A2</font></span>: 
<font color="Maroon" title="c6">s2</font> <a href="modelc_3.html#R6" title="MODELC_3:pred.6">is_next_of</a> <font color="Maroon" title="c4">s1</font>
 <span class="kw">and </span><br/><a NAME="E3:97"/><span class="lab"><font color="Green" title="E88">A3</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> or ( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">F1</font> = <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c8">L</font> being   <a href="finseq_1.html#NM1" title="FINSEQ_1:NM.1">FinSequence</a><span class="kw"> such that </span><br/><a NAME="E5:97"/><span class="lab"><font color="Green" title="E89">A4</font></span>: 
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="c8">L</font>
 <span class="kw">and </span><br/><a NAME="E6:97"/><span class="lab"><font color="Green" title="E90">A5</font></span>: 
<font color="Maroon" title="c8">L</font> <a href="modelc_3.html#R5" title="MODELC_3:pred.5">is_Finseq_for</a> <font color="Maroon" title="c3">v</font>
 <span class="kw">and </span><br/><a NAME="E7:97"/><span class="lab"><font color="Green" title="E91">A6</font></span>: 
<font color="Maroon" title="c8">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c5">s0</font>
 <span class="kw">and </span><br/><a NAME="E8:97"/><span class="lab"><font color="Green" title="E92">A7</font></span>: 
<font color="Maroon" title="c8">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="c8">L</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97"><span class="lab"><font color="Green" title="E86">A1</font></span></a>, <a class="ref" href="modelc_3.html#D20" target="_self" title="MODELC_3:def.20">Def20</a></span>;<br/>
<a NAME="E9:97"/><span class="lab"><font color="Green" title="E93">A8</font></span>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c8">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1</span>)</span>,<font color="Maroon" title="c3">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K12" title="MODELC_3:func.12">'X'</a> <font color="Maroon" title="c5">s0</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:97"><span class="lab"><font color="Green" title="E91">A6</font></span></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">Def16</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">n</font> =  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">L</font>;<br/>
<a NAME="E10:97"/><span class="lab"><font color="Green" title="E94">A9</font></span>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c8">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="c8">L</font></span>)</span></span>)</span>,<font color="Maroon" title="c3">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:97"><span class="lab"><font color="Green" title="E92">A7</font></span></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">Def16</a></span>;<br/>
<a NAME="E11:97"/>
1 <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="c8">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E88">A3</font></span></a>, <a class="txt" href="#E5:97"><span class="lab"><font color="Green" title="E89">A4</font></span></a>, <a class="txt" href="#E7:97"><span class="lab"><font color="Green" title="E91">A6</font></span></a>, <a class="txt" href="#E8:97"><span class="lab"><font color="Green" title="E92">A7</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c10">m</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a><span class="kw"> such that </span><br/><a NAME="E13:97"/><span class="lab"><font color="Green" title="E95">A10</font></span>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font> &amp; <font color="Maroon" title="c10">m</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="c8">L</font> )
 <span class="kw">and </span><br/><a NAME="E14:97"/><span class="lab"><font color="Green" title="E96">A11</font></span>: 
(  not <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c8">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c3">v</font>)</span>)</span> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c8">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c10">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> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97"><span class="lab"><font color="Green" title="E88">A3</font></span></a>, <a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E90">A5</font></span></a>, <a class="txt" href="#E10:97"><span class="lab"><font color="Green" title="E94">A9</font></span></a>, <a class="txt" href="#E9:97"><span class="lab"><font color="Green" title="E93">A8</font></span></a>, <a class="ref" href="modelc_3.html#T27" target="_self" title="MODELC_3:th.27">Th27</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">N1</font>, <font color="Maroon" title="c12">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><span class="kw"> such that </span><br/><a NAME="E16:97"/><span class="lab"><font color="Green" title="E97">A12</font></span>: 
<font color="Maroon" title="c11">N1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font>
 <span class="kw">and </span><br/><a NAME="E17:97"/><span class="lab"><font color="Green" title="E98">A13</font></span>: 
<font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>
 <span class="kw">and </span><br/><a NAME="E18:97"/><span class="lab"><font color="Green" title="E99">A14</font></span>: 
<font color="Maroon" title="c12">N2</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c11">N1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E90">A5</font></span></a>, <a class="txt" href="#E13:97"><span class="lab"><font color="Green" title="E95">A10</font></span></a>, <a class="ref" href="modelc_3.html#D19" target="_self" title="MODELC_3:def.19">Def19</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">m1</font> = <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1;<br/>
<a NAME="E19:97"/><span class="lab"><font color="Green" title="E100">A15</font></span>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c8">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c10">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>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">N2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:97"><span class="lab"><font color="Green" title="E98">A13</font></span></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">Def16</a></span>;<br/>
<a NAME="E20:97"/><span class="lab"><font color="Green" title="E101">A16</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D16" title="MODELC_2:def.16">MODELC_2:def 16</a></span>;<br/>
<a NAME="E21:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A17</font></span>: 
 <a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D3" target="_self" title="MODELC_3:def.3">Def3</a></span>;<br/>
<a NAME="E22:97"/>
 <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:97"><span class="lab"><font color="Green" title="E101">A16</font></span></a>, <a class="ref" href="modelc_2.html#D20" title="MODELC_2:def.20">MODELC_2:def 20</a></span>;<br/>
<a NAME="E23:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E103">A18</font></span>: 
 <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">G</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:97"><span class="lab"><font color="Green" title="E101">A16</font></span></a>, <a class="ref" href="modelc_3.html#D2" target="_self" title="MODELC_3:def.2">Def2</a></span>;<br/>
<a NAME="E24:97"/>
 <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:97"><span class="lab"><font color="Green" title="E101">A16</font></span></a>, <a class="ref" href="modelc_2.html#D19" title="MODELC_2:def.19">MODELC_2:def 19</a></span>;<br/>
<a NAME="E25:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E104">A19</font></span>: 
 <a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c1">F</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:97"><span class="lab"><font color="Green" title="E101">A16</font></span></a>, <a class="ref" href="modelc_3.html#D1" target="_self" title="MODELC_3:def.1">Def1</a></span>;<br/>
<a NAME="E26:97"/><span class="lab"><font color="Green" title="E105">A20</font></span>: 
 <a href="modelc_3.html#K10" title="MODELC_3:func.10">CastNode</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c8">L</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c10">m</font></span>)</span>,<font color="Maroon" title="c3">v</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">N1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:97"><span class="lab"><font color="Green" title="E97">A12</font></span></a>, <a class="ref" href="modelc_3.html#D16" target="_self" title="MODELC_3:def.16">Def16</a></span>;<br/>
<a NAME="E27:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E106">A21</font></span>: 
 the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">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 <font color="Maroon" title="c4">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E90">A5</font></span></a>, <a class="txt" href="#E10:97"><span class="lab"><font color="Green" title="E94">A9</font></span></a>, <a class="txt" href="#E13:97"><span class="lab"><font color="Green" title="E95">A10</font></span></a>, <a class="ref" href="modelc_3.html#T31" target="_self" title="MODELC_3:th.31">Th31</a></span>;<br/>
<a NAME="E28:97"/><span class="lab"><font color="Green" title="E107">A22</font></span>: 
( <font color="Maroon" title="c10">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>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">L</font> &amp; 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c10">m</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:97"><span class="lab"><font color="Green" title="E95">A10</font></span></a>, <a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></span>;<br/>
<a NAME="E29:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E108">A23</font></span>: 
 the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c12">N2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c4">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E90">A5</font></span></a>, <a class="txt" href="#E10:97"><span class="lab"><font color="Green" title="E94">A9</font></span></a>, <a class="txt" href="#E19:97"><span class="lab"><font color="Green" title="E100">A15</font></span></a>, <a class="ref" href="modelc_3.html#T31" target="_self" title="MODELC_3:th.31">Th31</a></span>;<br/>
<a NAME="E30:97"/>
 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="c8">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="c8">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>  <a href="modelc_3.html#K7" title="MODELC_3:func.7">{}</a> <font color="Maroon" title="c3">v</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:97"><span class="lab"><font color="Green" title="E94">A9</font></span></a>, <a class="ref" href="modelc_3.html#D11" target="_self" title="MODELC_3:def.11">Def11</a></span>;<br/>
<a NAME="E31:97"/><span class="kw">then </span><span class="lab"><font color="Green" title="E109">A24</font></span>: 
 the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">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 <font color="Maroon" title="c4">s1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97"><span class="lab"><font color="Green" title="E90">A5</font></span></a>, <a class="txt" href="#E10:97"><span class="lab"><font color="Green" title="E94">A9</font></span></a>, <a class="txt" href="#E19:97"><span class="lab"><font color="Green" title="E100">A15</font></span></a>, <a class="txt" href="#E28:97"><span class="lab"><font color="Green" title="E107">A22</font></span></a>, <a class="ref" href="modelc_3.html#T34" target="_self" title="MODELC_3:th.34">Th34</a></span>;<br/>
<a NAME="E32:97"/><span class="lab"><font color="Green" title="E110">A25</font></span>: 
<font color="Maroon" title="c12">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c11">N1</font>,<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:97"><span class="lab"><font color="Green" title="E96">A11</font></span></a>, <a class="txt" href="#E18:97"><span class="lab"><font color="Green" title="E99">A14</font></span></a>, <a class="txt" href="#E26:97"><span class="lab"><font color="Green" title="E105">A20</font></span></a>, <a class="txt" href="#E19:97"><span class="lab"><font color="Green" title="E100">A15</font></span></a>, <a class="ref" href="modelc_3.html#T28" target="_self" title="MODELC_3:th.28">Th28</a></span>;<br/>
<a NAME="E33:97"/>
(  not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> implies ( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> ) )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:97_1"/><span class="lab"><font color="Green" title="E111">A26</font></span>: 
 not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:97_1_1_1"/>
( ( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> &amp; <font color="Maroon" title="c12">N2</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"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>,<font color="Maroon" title="c11">N1</font>) ) or ( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> &amp; ( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  or <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  or <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>  ) &amp; <font color="Maroon" title="c12">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"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>,<font color="Maroon" title="c11">N1</font>) ) )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E32:97"><span class="lab"><font color="Green" title="E110">A25</font></span></a>, <a class="ref" href="modelc_3.html#D6" target="_self" title="MODELC_3:def.6">Def6</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_1_1"/><span class="lab"><font color="Green" title="E112">A27</font></span>: 
( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> &amp; <font color="Maroon" title="c12">N2</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"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>,<font color="Maroon" title="c11">N1</font>) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )</span><br/><div class="add"><a NAME="E2:97_1_1_1_1"/><span class="kw">then </span>
 the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">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="c11">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"><span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def4</a></span>;<br/><a NAME="E3:97_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E113">A28</font></span>: 
<span class="p1">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E4:97_1_1_1_1"/><span class="lab"><font color="Green" title="E114">A29</font></span>: 
<font color="Maroon" title="c1">F</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="c4">s1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_1_1_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:97_1_1_1_1_1_1_1"/>
( <font color="Maroon" title="c1">F</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="c11">N1</font> or  not <font color="Maroon" title="c1">F</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="c11">N1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c1">F</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="c11">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">F</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="c4">s1</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:97_1_1_1_1_1_1_1_1"/>
<font color="Maroon" title="c1">F</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="c4">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:97"><span class="lab"><font color="Green" title="E106">A21</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_1_1_1_1_1_2"/><span class="lab"><font color="Green" title="E115">A30</font></span>: 
 not <font color="Maroon" title="c1">F</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="c11">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">F</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="c4">s1</font></span><br/><div class="add"><a NAME="E2:97_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:97"><span class="lab"><font color="Green" title="E104">A19</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:97_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1_1_1_1_1_1_1_2"><span class="lab"><font color="Green" title="E115">A30</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E4:97_1_1_1_1_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">F</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="c12">N2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97_1_1_1_1"><span class="lab"><font color="Green" title="E113">A28</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:97_1_1_1_1_1_1_1_2"/>
<font color="Maroon" title="c1">F</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="c4">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:97"><span class="lab"><font color="Green" title="E109">A24</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:97_1_1_1_1_1"/>
<font color="Maroon" title="c1">F</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="c4">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><a NAME="E5:97_1_1_1_1"/>
 the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c12">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c11">N1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1_1_1_1"><span class="lab"><font color="Green" title="E112">A27</font></span></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def4</a></span>;<br/><a NAME="E6:97_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E115">A31</font></span>: 
 <a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c12">N2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E7:97_1_1_1_1"/>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E21:97"><span class="lab"><font color="Green" title="E102">A17</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E8:97_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c12">N2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97_1_1_1_1"><span class="lab"><font color="Green" title="E115">A31</font></span></a></span>;<br/><a NAME="E9:97_1_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E116">A32</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c4">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E29:97"><span class="lab"><font color="Green" title="E108">A23</font></span></a></span>;<br/><a NAME="E10:97_1_1_1_1"/>
 the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c4">s1</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 <font color="Maroon" title="c6">s2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97"><span class="lab"><font color="Green" title="E87">A2</font></span></a>, <a class="ref" href="modelc_3.html#T37" target="_self" title="MODELC_3:th.37">Th37</a></span>;<br/><span class="kw">hence </span><a NAME="E11:97_1_1_1_1"/>
( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:97_1_1_1_1"><span class="lab"><font color="Green" title="E114">A29</font></span></a>, <a class="txt" href="#E9:97_1_1_1_1"><span class="lab"><font color="Green" title="E116">A32</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_1_2"/>
( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c11">N1</font> &amp; ( <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  or <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  or <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>  ) &amp; <font color="Maroon" title="c12">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"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>,<font color="Maroon" title="c11">N1</font>) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )</span><br/><div class="add"><a NAME="E2:97_1_1_1_2"/><span class="kw">then </span>
 the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">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="c11">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"><span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/><a NAME="E3:97_1_1_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E112">A33</font></span>: 
<span class="p1">(<span class="default"><a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></span>;<br/><a NAME="E4:97_1_1_1_2"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="97_1_1_1_2_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_2_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:97_1_1_1_2_1_1_1"/>
( <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> or  not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_2_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:97_1_1_1_2_1_1_1_1"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:97"><span class="lab"><font color="Green" title="E106">A21</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="97_1_1_1_2_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:97_1_1_1_2_1_1_1_2"/><span class="lab"><font color="Green" title="E113">A34</font></span>: 
 not <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font></span><br/><div class="add"><a NAME="E2:97_1_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:97"><span class="lab"><font color="Green" title="E103">A18</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:97_1_1_1_2_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font></span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c11">N1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1_1_1_2_1_1_1_2"><span class="lab"><font color="Green" title="E113">A34</font></span></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><a NAME="E4:97_1_1_1_2_1_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c12">N2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97_1_1_1_2"><span class="lab"><font color="Green" title="E112">A33</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E5:97_1_1_1_2_1_1_1_2"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:97"><span class="lab"><font color="Green" title="E109">A24</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:97_1_1_1_2_1"/>
<font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E5:97_1_1_1_2"/>
( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1"><span class="lab"><font color="Green" title="E111">A26</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:97_1"/>
( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E34:97"/>
( <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">s1</font> or ( <font color="Maroon" title="c1">F</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="c4">s1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="modelc_2.html#K7" title="MODELC_2:func.7">'U'</a> <font color="Maroon" title="c2">G</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c6">s2</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
