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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">w</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="modelc_2.html#K27" title="MODELC_2:func.27">Inf_seq</a> <a href="modelc_2.html#K46" title="MODELC_2:func.46">AtomicFamily</a>   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/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#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/>







<b>assume </b><b>that </b><br/><a NAME="E1:39"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N</font>
 <b>and </b><br/><a NAME="E2:39"/><i><font color="Green" title="E33">A2</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>set </b><font color="Maroon" title="c5">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/>
<b>set </b><font color="Maroon" title="c6">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/>
<b>set </b><font color="Maroon" title="c7">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/>
<b>set </b><font color="Maroon" title="c8">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/>
<b>set </b><font color="Maroon" title="c9">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/>
<b>set </b><font color="Maroon" title="c10">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/>
<b>set </b><font color="Maroon" title="c11">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/>
<b>set </b><font color="Maroon" title="c12">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/>
<b>set </b><font color="Maroon" title="c13">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/>
<b>set </b><font color="Maroon" title="c14">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/>
<b>set </b><font color="Maroon" title="c15">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/>
<b>set </b><font color="Maroon" title="c16">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/>
<b>set </b><font color="Maroon" title="c17">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/>
<b>set </b><font color="Maroon" title="c18">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/>
<a NAME="E3:39"/><i><font color="Green" title="E34">A3</font></i>: 
<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>
 
<b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a>, <a class="txt" href="#E1:39"><i><font color="Green" title="E32">A1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c19">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/>
<b>set </b><font color="Maroon" title="c20">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/>
<a NAME="E4:39"/>
<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>
 
<b>by </b><i><a class="txt" href="#E2:39"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="modelc_2.html#T7" title="MODELC_2:th.7">MODELC_2:7</a></i>;<br/>
<a NAME="E5:39"/><b>then </b><i><font color="Green" title="E35">A4</font></i>: 
( <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> ) )
 
<b>by </b><i><a class="ref" href="modelc_2.html#T66" title="MODELC_2:th.66">MODELC_2:66</a></i>;<br/>
<a NAME="E6:39"/><i><font color="Green" title="E36">A5</font></i>: 
 <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>
 
<b>by </b><i><a class="txt" href="#E2:39"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="modelc_3.html#D1" target="_self" title="MODELC_3:def.1">Def203</a></i>;<br/>
<a NAME="E7:39"/><i><font color="Green" title="E37">A6</font></i>: 
 <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="modelc_2.html#K12" title="MODELC_2:func.12">the_right_argument_of</a> <font color="Maroon" title="c1">H</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="#E2:39"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="modelc_3.html#D2" target="_self" title="MODELC_3:def.2">Def204</a></i>;<br/>
<a NAME="E8:39"/><i><font color="Green" title="E38">A7</font></i>: 
 <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> 
 
<b>by </b><i><a class="txt" href="#E2:39"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="modelc_3.html#D3" target="_self" title="MODELC_3:def.3">Def205</a></i>;<br/>
<a NAME="E9:39"/><i><font color="Green" title="E39">A8</font></i>: 
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#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>
 
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def206</a></i>;<br/>
<a NAME="E10:39"/><i><font color="Green" title="E40">A9</font></i>: 
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#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>
 
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def206</a>, <a class="txt" href="#E6:39"><i><font color="Green" title="E36">A5</font></i></a></i>;<br/>
<i><font color="Green" title="E41">A10</font></i>: 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> 
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E32">A1</font></i></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def206</a>, <a class="txt" href="#E8:39"><i><font color="Green" title="E38">A7</font></i></a></i>
<br/>.= 
the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N</font>

;<br/>
<a NAME="E12:39"/><i><font color="Green" title="E42">A11</font></i>: 
the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#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>
 
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="#E2:39"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def207</a></i>;<br/>
<a NAME="E13:39"/><i><font color="Green" title="E43">A12</font></i>: 
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#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>
 
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="#E2:39"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def207</a>, <a class="txt" href="#E7:39"><i><font color="Green" title="E37">A6</font></i></a></i>;<br/>
<a NAME="E14:39"/><i><font color="Green" title="E44">A13</font></i>: 
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>
 
<b>by </b><i><a class="txt" href="#E1:39"><i><font color="Green" title="E32">A1</font></i></a>, <a class="txt" href="#E2:39"><i><font color="Green" title="E33">A2</font></i></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def207</a></i>;<br/>
<a NAME="E15:39"/><i><font color="Green" title="E45">Alem1</font></i>: 
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"><b>proof </b></a><div class="add">

<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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#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="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><br/>

<b>assume </b><a NAME="E1:39_2"/><i><font color="Green" title="E46">B1</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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#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"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_2_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#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="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> 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#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><b>by </b><i><a class="txt" href="#E1:39_2"><i><font color="Green" title="E46">B1</font></i></a>, <a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_1_1_1"><b>suppose </b></a><a NAME="E1:39_2_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#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:()"><i><font color="Red">::  thesis: </font></i></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#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"/><b>then </b>
( <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> )
 <b>by </b><i><a class="txt" href="#E9:39"><i><font color="Green" title="E39">A8</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E3:39_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> <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> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a>, <a class="txt" href="#E3:39"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_1_1_2"><b>suppose </b></a><a NAME="E1:39_2_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#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:()"><i><font color="Red">::  thesis: </font></i></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#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"/><b>then </b>
( <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#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> )
 <b>by </b><i><a class="txt" href="#E10:39"><i><font color="Green" title="E40">A9</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:39_2_1_1_2"/><b>then </b>
( <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#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> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><b>hence </b><a NAME="E4:39_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> <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> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_2_1_1_3"><b>suppose </b></a><a NAME="E1:39_2_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#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:()"><i><font color="Red">::  thesis: </font></i></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#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c22">G</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E3:39_2_1_1_3"/><i><font color="Green" title="E47">C1</font></i>: 
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">G</font>
 <b>and </b><br/><a NAME="E4:39_2_1_1_3"/><i><font color="Green" title="E48">C2</font></i>: 
 ex <font color="Olive" title="b1">G1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Olive" title="b1">G1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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="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="c22">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Olive" title="b1">G1</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c23">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E6:39_2_1_1_3"/><i><font color="Green" title="E49">C3</font></i>: 
<font color="Maroon" title="c23">G1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <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>
 <b>and </b><br/><a NAME="E7:39_2_1_1_3"/><i><font color="Green" title="E50">C4</font></i>: 
<font color="Maroon" title="c22">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c23">G1</font>
 <b>by </b><i><a class="txt" href="#E4:39_2_1_1_3"><i><font color="Green" title="E48">C2</font></i></a></i>;<br/><a NAME="E8:39_2_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 <font color="Maroon" title="c3">N</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:39_2_1_1_3"><i><font color="Green" title="E47">C1</font></i></a>, <a class="txt" href="#E7:39_2_1_1_3"><i><font color="Green" title="E50">C4</font></i></a>, <a class="txt" href="#E6:39_2_1_1_3"><i><font color="Green" title="E49">C3</font></i></a>, <a class="txt" href="#E11:39"><i><font color="Green" title="E41">A10</font></i></a></i>;<br/><b>hence </b><a NAME="E9:39_2_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#K11" title="MODELC_2:func.11">the_left_argument_of</a> <font color="Maroon" title="c1">H</font> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:39_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#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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E16:39"/><i><font color="Green" title="E46">Alem2</font></i>: 
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"><b>proof </b></a><div class="add">

<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E1:39_3"/><i><font color="Green" title="E47">B1</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></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><b>by </b><i><a class="txt" href="#E1:39_3"><i><font color="Green" title="E47">B1</font></i></a>, <a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_3_1_1_1"><b>suppose </b></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:()"><i><font color="Red">::  thesis: </font></i></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"/><b>then </b>
( <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> )
 <b>by </b><i><a class="txt" href="#E12:39"><i><font color="Green" title="E42">A11</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="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> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a>, <a class="txt" href="#E3:39"><i><font color="Green" title="E34">A3</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_3_1_1_2"><b>suppose </b></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:()"><i><font color="Red">::  thesis: </font></i></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"/><b>then </b>
( <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> )
 <b>by </b><i><a class="txt" href="#E13:39"><i><font color="Green" title="E43">A12</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E3:39_3_1_1_2"/><b>then </b>
( <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> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><b>hence </b><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> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_3_1_1_3"><b>suppose </b></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:()"><i><font color="Red">::  thesis: </font></i></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"><b>then consider </b><font color="Maroon" title="c22">G</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E3:39_3_1_1_3"/><i><font color="Green" title="E48">C1</font></i>: 
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">G</font>
 <b>and </b><br/><a NAME="E4:39_3_1_1_3"/><i><font color="Green" title="E49">C2</font></i>: 
 ex <font color="Olive" title="b1">G1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Olive" title="b1">G1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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="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> &amp; <font color="Maroon" title="c22">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Olive" title="b1">G1</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c23">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E6:39_3_1_1_3"/><i><font color="Green" title="E50">C3</font></i>: 
<font color="Maroon" title="c23">G1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <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>
 <b>and </b><br/><a NAME="E7:39_3_1_1_3"/><i><font color="Green" title="E51">C4</font></i>: 
<font color="Maroon" title="c22">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c23">G1</font>
 <b>by </b><i><a class="txt" href="#E4:39_3_1_1_3"><i><font color="Green" title="E49">C2</font></i></a></i>;<br/><a NAME="E8:39_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 <font color="Maroon" title="c3">N</font></span>)</span>
 <b>by </b><i><a class="txt" href="#E3:39_3_1_1_3"><i><font color="Green" title="E48">C1</font></i></a>, <a class="txt" href="#E7:39_3_1_1_3"><i><font color="Green" title="E51">C4</font></i></a>, <a class="txt" href="#E6:39_3_1_1_3"><i><font color="Green" title="E50">C3</font></i></a>, <a class="txt" href="#E14:39"><i><font color="Green" title="E44">A13</font></i></a></i>;<br/><b>hence </b><a NAME="E9:39_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> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E17:39"/><i><font color="Green" title="E47">Alem3</font></i>: 
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_4"><b>proof </b></a><div class="add">

<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E1:39_4"/><i><font color="Green" title="E48">B1</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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_4_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_4_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_4_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><b>by </b><i><a class="txt" href="#E1:39_4"><i><font color="Green" title="E48">B1</font></i></a>, <a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_4_1_1_1"><b>suppose </b></a><a NAME="E1:39_4_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:()"><i><font color="Red">::  thesis: </font></i></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_4_1_1_1"/><b>then </b>
( <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> )
 <b>by </b><i><a class="txt" href="#E9:39"><i><font color="Green" title="E39">A8</font></i></a>, <a class="txt" href="#E12:39"><i><font color="Green" title="E42">A11</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E3:39_4_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> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_4_1_1_2"><b>suppose </b></a><a NAME="E1:39_4_1_1_2"/><i><font color="Green" title="E49">C2</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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_4_1_1_2_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_4_1_1_2_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_4_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_4_1_1_2_1_1_1"><b>suppose </b></a><a NAME="E1:39_4_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:()"><i><font color="Red">::  thesis: </font></i></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_4_1_1_2_1_1_1"/><b>then </b>
<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>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:39_4_1_1_2_1_1_1"/><b>then </b>
( <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> )
 <b>by </b><i><a class="txt" href="#E9:39"><i><font color="Green" title="E39">A8</font></i></a>, <a class="txt" href="#E12:39"><i><font color="Green" title="E42">A11</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E4:39_4_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> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_4_1_1_2_1_1_2"><b>suppose </b></a><a NAME="E1:39_4_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:()"><i><font color="Red">::  thesis: </font></i></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_4_1_1_2_1_1_2"/><b>then </b>
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>
 <b>by </b><i><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/><a NAME="E3:39_4_1_1_2_1_1_2"/><b>then </b>
<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>
 <b>by </b><i><a class="txt" href="#E1:39_4_1_1_2"><i><font color="Green" title="E49">C2</font></i></a>, <a class="ref" href="xboole_0.html#D5" title="XBOOLE_0:def.5">XBOOLE_0:def 5</a></i>;<br/><a NAME="E4:39_4_1_1_2_1_1_2"/><b>then </b>
( <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> )
 <b>by </b><i><a class="txt" href="#E10:39"><i><font color="Green" title="E40">A9</font></i></a>, <a class="txt" href="#E13:39"><i><font color="Green" title="E43">A12</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>hence </b><a NAME="E5:39_4_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> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div><b>hence </b><a NAME="E3:39_4_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_4_1_1_3"><b>suppose </b></a><a NAME="E1:39_4_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 <font color="Maroon" title="c3">N</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="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"><b>then consider </b><font color="Maroon" title="c22">G</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E3:39_4_1_1_3"/><i><font color="Green" title="E49">C1</font></i>: 
<font color="Maroon" title="c21">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c22">G</font>
 <b>and </b><br/><a NAME="E4:39_4_1_1_3"/><i><font color="Green" title="E50">C2</font></i>: 
 ex <font color="Olive" title="b1">G1</font> being  <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a> st <br/>( <font color="Olive" title="b1">G1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <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> &amp; <font color="Maroon" title="c22">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Olive" title="b1">G1</font> )
 ;<br/><b>consider </b><font color="Maroon" title="c23">G1</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E6:39_4_1_1_3"/><i><font color="Green" title="E51">C3</font></i>: 
<font color="Maroon" title="c23">G1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N</font>
 <b>and </b><br/><a NAME="E7:39_4_1_1_3"/><i><font color="Green" title="E52">C4</font></i>: 
<font color="Maroon" title="c22">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_2.html#K6" title="MODELC_2:func.6">'X'</a> <font color="Maroon" title="c23">G1</font>
 <b>by </b><i><a class="txt" href="#E4:39_4_1_1_3"><i><font color="Green" title="E50">C2</font></i></a></i>;<br/><a NAME="E8:39_4_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#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> &amp; <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> )
 <b>by </b><i><a class="txt" href="#E3:39_4_1_1_3"><i><font color="Green" title="E49">C1</font></i></a>, <a class="txt" href="#E7:39_4_1_1_3"><i><font color="Green" title="E52">C4</font></i></a>, <a class="txt" href="#E6:39_4_1_1_3"><i><font color="Green" title="E51">C3</font></i></a>, <a class="txt" href="#E11:39"><i><font color="Green" title="E41">A10</font></i></a>, <a class="txt" href="#E14:39"><i><font color="Green" title="E44">A13</font></i></a></i>;<br/><b>hence </b><a NAME="E9:39_4_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> )
 <b>by </b><i><a class="txt" href="modelc_3.html#E1"><i><font color="Green" title="E1">LemSUM01</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:39_4"/>
( <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E18:39"/><i><font color="Green" title="E48">A17</font></i>: 
(  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_5"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_5"/><i><font color="Green" title="E49">B1</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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_5_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_5_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_5_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><b>by </b><i><a class="txt" href="#E1:39_5"><i><font color="Green" title="E49">B1</font></i></a>, <a class="txt" href="#E3:39"><i><font color="Green" title="E34">A3</font></i></a>, <a class="txt" href="#E5:39"><i><font color="Green" title="E35">A4</font></i></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_5_1_1_1"><b>suppose </b></a><a NAME="E1:39_5_1_1_1"/><i><font color="Green" title="E50">B3</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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_5_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_5_1_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E1:39_5_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:()"><i><font color="Red">::  thesis: </font></i></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_5_1_1_1_1"/><b>then </b>
( <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> )
 
<b>by </b><i><a class="txt" href="#E15:39"><i><font color="Green" title="E45">Alem1</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:39_5_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>
 <b>by </b><i><a class="txt" href="#E1:39_5"><i><font color="Green" title="E49">B1</font></i></a>, <a class="txt" href="#E1:39_5_1_1_1"><i><font color="Green" title="E50">B3</font></i></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:39_5_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> )
 <b>by </b><i><a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_5_1_1_2"><b>suppose </b></a><a NAME="E1:39_5_1_1_2"/><i><font color="Green" title="E50">B4</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></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_5_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_5_1_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E1:39_5_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:()"><i><font color="Red">::  thesis: </font></i></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_5_1_1_2_1"/><b>then </b>
( <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> )
 
<b>by </b><i><a class="txt" href="#E16:39"><i><font color="Green" title="E46">Alem2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:39_5_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>
 <b>by </b><i><a class="txt" href="#E1:39_5"><i><font color="Green" title="E49">B1</font></i></a>, <a class="txt" href="#E1:39_5_1_1_2"><i><font color="Green" title="E50">B4</font></i></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:39_5_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> )
 <b>by </b><i><a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E3:39_5"/>
( <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></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"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_6"/><i><font color="Green" title="E49">B1</font></i>: 
( <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:()"><i><font color="Red">::  thesis: </font></i></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"><b>proof </b></a><div class="add">

<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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/>

<b>assume </b><a NAME="E1:39_6_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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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"/><b>then </b><i><font color="Green" title="E50">C1</font></i>: 
( <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> )
 
<b>by </b><i><a class="txt" href="#E17:39"><i><font color="Green" title="E47">Alem3</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_6_1_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_6_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:39_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><b>by </b><i><a class="txt" href="#E1:39_6"><i><font color="Green" title="E49">B1</font></i></a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_6_1_1_1_1"><b>suppose </b></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:()"><i><font color="Red">::  thesis: </font></i></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"><b>hence </b><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>
 <b>by </b><i><a class="txt" href="#E2:39_6_1"><i><font color="Green" title="E50">C1</font></i></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="39_6_1_1_1_2"><b>suppose </b></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:()"><i><font color="Red">::  thesis: </font></i></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"><b>hence </b><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>
 <b>by </b><i><a class="txt" href="#E2:39_6_1"><i><font color="Green" title="E50">C1</font></i></a>, <a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div></div><b>end;</b></div></div><b>end;</b></div>
<b>hence </b><a NAME="E4:39_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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:39_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>
 <b>by </b><i><a class="ref" href="modelc_2.html#D66" title="MODELC_2:def.66">MODELC_2:def 66</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="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> ) )
 <b>by </b><i><a class="txt" href="#E18:39"><i><font color="Green" title="E48">A17</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
