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<span class="kw">let </span><font color="Maroon" title="c1">H</font>, <font color="Maroon" title="c2">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="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">N</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="c2">v</font><br/> for <font color="Olive" title="b2">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>   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#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Olive" title="b1">N</font> &amp; <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  holds <br/>( <font color="Olive" title="b2">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Olive" title="b1">N</font> iff ( <font color="Olive" title="b2">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Olive" title="b1">N</font></span>)</span> or <font color="Olive" title="b2">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Olive" title="b1">N</font></span>)</span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">N</font> be   <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="c2">v</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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>   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#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  holds <br/>( <font color="Olive" title="b1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> iff ( <font color="Olive" title="b1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Olive" title="b1">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> ) )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N</font> &amp; <font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  implies ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> iff ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> ) ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:39"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<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="c3">N</font>
 <span class="kw">and </span><br/><a NAME="E2:39"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<font color="Maroon" title="c1">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> iff ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> ) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c5">NN</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">NO</font> = the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">SN2</font> =  <a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">NX</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">SN1</font> =  <a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font>;<br/>
<a NAME="E3:39"/><span class="lab"><font color="Green" title="E34">A3</font></span>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">SN1X</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>;<br/>
<a NAME="E4:39"/>
 <a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="modelc_3.html#D3" target="_self" title="MODELC_3:def.3">Def3</a></span>;<br/>
<span class="kw">then </span><span class="lab"><font color="Green" title="E35">A4</font></span>: the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> = 
the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def4</a></span>
<br/>.= 
the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N</font>

;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">H1</font> =  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">XSN1X</font> =  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c13">SN1N</font> = 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#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c14">SN1O</font> = 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#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>;<br/>
<a NAME="E6:39"/><span class="lab"><font color="Green" title="E36">A5</font></span>: 
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#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</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 <font color="Maroon" title="c3">N</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"><font color="Maroon" title="c1">H</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="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def4</a></span>;<br/>
<a NAME="E7:39"/>
 <a href="modelc_3.html#K2" title="MODELC_3:func.2">LTLNew1</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#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</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="txt" href="#E2:39"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="modelc_3.html#D1" target="_self" title="MODELC_3:def.1">Def1</a></span>;<br/>
<a NAME="E8:39"/><span class="kw">then </span><span class="lab"><font color="Green" title="E37">A6</font></span>: 
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#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> <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="c3">N</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#K11" title="MODELC_2:func.11">the_left_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="c3">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def4</a></span>;<br/>
<a NAME="E9:39"/><span class="lab"><font color="Green" title="E38">A7</font></span>: 
for <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  holds <br/>(  not <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c15">F</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="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:39_2"/><span class="lab"><font color="Green" title="E39">A8</font></span>: 
<font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_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="E1:39_2_1_1"/>
( <font color="Maroon" title="c15">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c15">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_2"><span class="lab"><font color="Green" title="E39">A8</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:39_2_1_1_1"/>
<font color="Maroon" title="c15">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/><div class="add"><a NAME="E2:39_2_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c15">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="c3">N</font> or <font color="Maroon" title="c15">F</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"><font color="Maroon" title="c1">H</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="#E6:39"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:39_2_1_1_1"/>
( <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="39_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:39_2_1_1_2"/>
<font color="Maroon" title="c15">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/><div class="add"><a NAME="E2:39_2_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c15">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="c3">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><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> or <font color="Maroon" title="c15">F</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#K11" title="MODELC_2:func.11">the_left_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="c3">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:39"><span class="lab"><font color="Green" title="E37">A6</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E3:39_2_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c15">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="c3">N</font> or <font color="Maroon" title="c15">F</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#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</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="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E4:39_2_1_1_2"/>
( <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="39_2_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:39_2_1_1_3"/>
<font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:39_2_1_1_3"/>
( <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:39"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E3:39_2"/>
( <font color="Maroon" title="c15">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c15">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">set </span><font color="Maroon" title="c15">XNX</font> =  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c16">SN2X</font> = the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c17">XSN2X</font> =  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c18">SN2O</font> = 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#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>;<br/>
<a NAME="E10:39"/><span class="lab"><font color="Green" title="E39">A9</font></span>: 
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#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</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 <font color="Maroon" title="c3">N</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"><font color="Maroon" title="c1">H</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="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c19">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/>
<span class="kw">set </span><font color="Maroon" title="c20">SN2N</font> = 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#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>;<br/>
<a NAME="E11:39"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="modelc_3.html#D2" target="_self" title="MODELC_3:def.2">Def2</a></span>;<br/>
<a NAME="E12:39"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A10</font></span>: 
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#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> <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="c3">N</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="c3">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/>
<a NAME="E13:39"/><span class="lab"><font color="Green" title="E41">A11</font></span>: 
the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> <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="c3">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/>
<a NAME="E14:39"/><span class="lab"><font color="Green" title="E42">A12</font></span>: 
for <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  holds <br/>(  not <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Olive" title="b1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_3"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c21">F</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="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:39_3"/><span class="lab"><font color="Green" title="E43">A13</font></span>: 
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_3_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_3_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="E1:39_3_1_1"/>
( <font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_3"><span class="lab"><font color="Green" title="E43">A13</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_3_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:39_3_1_1_1"/>
<font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/><div class="add"><a NAME="E2:39_3_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c21">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="c3">N</font> or <font color="Maroon" title="c21">F</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"><font color="Maroon" title="c1">H</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="#E10:39"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:39_3_1_1_1"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="39_3_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:39_3_1_1_2"/>
<font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/><div class="add"><a NAME="E2:39_3_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c21">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="c3">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><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> or <font color="Maroon" title="c21">F</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="c3">N</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:39"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E3:39_3_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c21">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="c3">N</font> or <font color="Maroon" title="c21">F</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> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></span>;<br/><span class="kw">hence </span><a NAME="E4:39_3_1_1_2"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="39_3_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:39_3_1_1_3"/>
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:39_3_1_1_3"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:39"><span class="lab"><font color="Green" title="E41">A11</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E3:39_3"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E15:39"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span> <a href="modelc_2.html#K5" title="MODELC_2:func.5">'or'</a> <span class="p1">(<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 class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="modelc_2.html#T7" title="MODELC_2:th.7">MODELC_2:7</a></span>;<br/>
<a NAME="E16:39"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A14</font></span>: 
( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c1">H</font> iff ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> or <font color="Maroon" title="c4">w</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> ) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#T66" title="MODELC_2:th.66">MODELC_2:66</a></span>;<br/>
<a NAME="E17:39"/><span class="lab"><font color="Green" title="E44">A15</font></span>: 
(  not <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_4"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:39_4"/><span class="lab"><font color="Green" title="E45">A16</font></span>: 
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_4_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_4_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="E1:39_4_1_1"/>
( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> or <font color="Maroon" title="c4">w</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> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39"><span class="lab"><font color="Green" title="E34">A3</font></span></a>, <a class="txt" href="#E16:39"><span class="lab"><font color="Green" title="E43">A14</font></span></a>, <a class="txt" href="#E1:39_4"><span class="lab"><font color="Green" title="E45">A16</font></span></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_4_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:39_4_1_1_1"/><span class="lab"><font color="Green" title="E46">A17</font></span>: 
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:39_4_1_1_1"/>
for <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> holds <br/><font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Olive" title="b1">F</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_4_1_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c21">F</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> implies <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:39_4_1_1_1_1"/>
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font></span><br/>

<a NAME="E2:39_4_1_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:39"><span class="lab"><font color="Green" title="E38">A7</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:39_4_1_1_1_1"/>
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_4"><span class="lab"><font color="Green" title="E45">A16</font></span></a>, <a class="txt" href="#E1:39_4_1_1_1"><span class="lab"><font color="Green" title="E46">A17</font></span></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:39_4_1_1_1"/>
( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="39_4_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:39_4_1_1_2"/><span class="lab"><font color="Green" title="E46">A18</font></span>: 
<font color="Maroon" title="c4">w</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:39_4_1_1_2"/>
for <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> holds <br/><font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Olive" title="b1">F</font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_4_1_1_2_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c21">F</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> implies <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:39_4_1_1_2_1"/>
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font></span><br/>

<a NAME="E2:39_4_1_1_2_1"/><span class="kw">then </span>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:39"><span class="lab"><font color="Green" title="E42">A12</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:39_4_1_1_2_1"/>
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_4"><span class="lab"><font color="Green" title="E45">A16</font></span></a>, <a class="txt" href="#E1:39_4_1_1_2"><span class="lab"><font color="Green" title="E46">A18</font></span></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div><span class="kw">hence </span><a NAME="E3:39_4_1_1_2"/>
( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E3:39_4"/>
( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E18:39"/><span class="lab"><font color="Green" title="E45">A19</font></span>: 
for <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> holds <br/>( <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_5"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c21">F</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> implies ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> ) )</span><br/>

<span class="kw">assume </span><a NAME="E1:39_5"/><span class="lab"><font color="Green" title="E46">A20</font></span>: 
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_5_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_5_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="E1:39_5_1_1"/>
( <font color="Maroon" title="c21">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="c3">N</font> or <font color="Maroon" title="c21">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="c3">N</font> or <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N</font></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_5"><span class="lab"><font color="Green" title="E46">A20</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_5_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:39_5_1_1_1"/>
<font color="Maroon" title="c21">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="c3">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:39_5_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:39"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="txt" href="#E10:39"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E3:39_5_1_1_1"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="39_5_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:39_5_1_1_2"/><span class="lab"><font color="Green" title="E47">A21</font></span>: 
<font color="Maroon" title="c21">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="c3">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )</span><br/><div class="add"><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_5_1_1_2_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_5_1_1_2_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="E1:39_5_1_1_2_1_1"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> or  not <font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">H</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_5_1_1_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:39_5_1_1_2_1_1_1"/>
<font color="Maroon" title="c21">F</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:39_5_1_1_2_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c21">F</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"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:39_5_1_1_2_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:39"><span class="lab"><font color="Green" title="E36">A5</font></span></a>, <a class="txt" href="#E10:39"><span class="lab"><font color="Green" title="E39">A9</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E4:39_5_1_1_2_1_1_1"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="39_5_1_1_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:39_5_1_1_2_1_1_2"/>
not <font color="Maroon" title="c21">F</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:39_5_1_1_2_1_1_2"/><span class="kw">then </span>
not <font color="Maroon" title="c21">F</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"><font color="Maroon" title="c1">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><a NAME="E3:39_5_1_1_2_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c21">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="c3">N</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_5_1_1_2"><span class="lab"><font color="Green" title="E47">A21</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="E4:39_5_1_1_2_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">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 <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:39"><span class="lab"><font color="Green" title="E37">A6</font></span></a>, <a class="txt" href="#E12:39"><span class="lab"><font color="Green" title="E40">A10</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><span class="kw">hence </span><a NAME="E5:39_5_1_1_2_1_1_2"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E3:39_5_1_1_2"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="39_5_1_1_3"><span class="kw">suppose </span></a><a NAME="E1:39_5_1_1_3"/><span class="lab"><font color="Green" title="E47">A22</font></span>: 
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )</span><br/><div class="add"><a NAME="E2:39_5_1_1_3"/><span class="kw">then </span>
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_2.html#K51" title="MODELC_2:func.51">'X'</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K13" title="MODELC_3:func.13">CastLTL</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <span class="p2">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/><span class="kw">hence </span><a NAME="E3:39_5_1_1_3"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:39"><span class="lab"><font color="Green" title="E35">A4</font></span></a>, <a class="txt" href="#E1:39_5_1_1_3"><span class="lab"><font color="Green" title="E47">A22</font></span></a>, <a class="txt" href="modelc_3.html#E1"><span class="lab"><font color="Green" title="E1">Lm1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E3:39_5"/>
( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> &amp; <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<a NAME="E19:39"/>
( ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> ) implies <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_6"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:39_6"/><span class="lab"><font color="Green" title="E46">A23</font></span>: 
( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font></span><br/>

<a NAME="E2:39_6"/>
for <font color="Olive" title="b1">F</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>  st <font color="Olive" title="b1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> holds <br/><font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Olive" title="b1">F</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_6_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c21">F</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="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> implies <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:39_6_1"/><span class="lab"><font color="Green" title="E47">A24</font></span>: 
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font></span><br/>

<a NAME="E2:39_6_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A25</font></span>: 
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:39"><span class="lab"><font color="Green" title="E45">A19</font></span></a></span>;<br/>
<a NAME="E3:39_6_1"/><span class="lab"><font color="Green" title="E49">A26</font></span>: 
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:39"><span class="lab"><font color="Green" title="E45">A19</font></span></a>, <a class="txt" href="#E1:39_6_1"><span class="lab"><font color="Green" title="E47">A24</font></span></a></span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_6_1_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_6_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="E1:39_6_1_1_1"/>
( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:39_6"><span class="lab"><font color="Green" title="E46">A23</font></span></a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_6_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:39_6_1_1_1_1"/>
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:39_6_1_1_1_1"/>
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:39_6_1"><span class="lab"><font color="Green" title="E49">A26</font></span></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="39_6_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:39_6_1_1_1_2"/>
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:39_6_1_1_1_2"/>
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:39_6_1"><span class="lab"><font color="Green" title="E48">A25</font></span></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  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="E5:39_6_1"/>
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R7" title="MODELC_2:pred.7">|=</a> <font color="Maroon" title="c21">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:39_6"/>
<font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E20:39"/>
( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <font color="Maroon" title="c3">N</font> iff ( <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> or <font color="Maroon" title="c4">w</font> <a href="modelc_2.html#R8" title="MODELC_2:pred.8">|=</a>  <a href="modelc_3.html#K14" title="MODELC_3:func.14">*</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> <font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c3">N</font></span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:39"><span class="lab"><font color="Green" title="E44">A15</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
