<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">F</font>, <font color="Maroon" title="c2">v</font> be   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">N2</font>, <font color="Olive" title="b2">N1</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>  st <font color="Olive" title="b1">N2</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Olive" title="b2">N1</font> &amp;  not <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b2">N1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b1">N2</font> holds <br/><font color="Olive" title="b1">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Olive" title="b2">N1</font>,<font color="Maroon" title="c1">F</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">N2</font>, <font color="Maroon" title="c4">N1</font> be   <a href="modelc_3.html#V1" title="MODELC_3:attr.1">strict</a>   <a href="modelc_3.html#L1" title="MODELC_3:struct.1">LTLnode</a> of <font color="Maroon" title="c2">v</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c4">N1</font> &amp;  not <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">N1</font> &amp; <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N2</font> implies <font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c4">N1</font>,<font color="Maroon" title="c1">F</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:83"/><span class="lab"><font color="Green" title="E72">A1</font></span>: 
<font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c4">N1</font>
 <span class="kw">and </span><br/><a NAME="E2:83"/><span class="lab"><font color="Green" title="E73">A2</font></span>: 
 not <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">N1</font>
 <span class="kw">and </span><br/><a NAME="E3:83"/><span class="lab"><font color="Green" title="E74">A3</font></span>: 
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c4">N1</font>,<font color="Maroon" title="c1">F</font></span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="83_1"><span class="kw">now </span></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:83_1_1"/>
( <font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R2" title="MODELC_3:pred.2">is_succ1_of</a> <font color="Maroon" title="c4">N1</font> or <font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R3" title="MODELC_3:pred.3">is_succ2_of</a> <font color="Maroon" title="c4">N1</font> )
 </span><span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:83"><span class="lab"><font color="Green" title="E72">A1</font></span></a>, <a class="ref" href="modelc_3.html#D9" target="_self" title="MODELC_3:def.9">Def9</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:83_1_1_1"/>
<font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R2" title="MODELC_3:pred.2">is_succ1_of</a> <font color="Maroon" title="c4">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c4">N1</font>,<font color="Maroon" title="c1">F</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><span class="kw"> such that </span><br/><a NAME="E3:83_1_1_1"/><span class="lab"><font color="Green" title="E75">A4</font></span>: 
( <font color="Maroon" title="c5">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="c4">N1</font> &amp; <font color="Maroon" title="c3">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K5" title="MODELC_3:func.5">SuccNode1</a> (<font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c4">N1</font>) )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D7" target="_self" title="MODELC_3:def.7">Def7</a></span>;<br/><a NAME="E4:83_1_1_1"/>
 the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">N1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:83_1_1_1"><span class="lab"><font color="Green" title="E75">A4</font></span></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def4</a></span>;<br/><a NAME="E5:83_1_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">N1</font> or <font color="Maroon" title="c1">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="c5">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:83"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E6:83_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E7:83_1_1_1"/>
<font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c4">N1</font>,<font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:83_1_1_1"><span class="lab"><font color="Green" title="E75">A4</font></span></a>, <a class="ref" href="modelc_3.html#D6" target="_self" title="MODELC_3:def.6">Def6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="83_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:83_1_1_2"/>
<font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R3" title="MODELC_3:pred.3">is_succ2_of</a> <font color="Maroon" title="c4">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c4">N1</font>,<font color="Maroon" title="c1">F</font></span><br/><div class="add"><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><span class="kw"> such that </span><br/><a NAME="E3:83_1_1_2"/><span class="lab"><font color="Green" title="E75">A5</font></span>: 
<font color="Maroon" title="c5">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="c4">N1</font>
 <span class="kw">and </span><br/><a NAME="E4:83_1_1_2"/><span class="lab"><font color="Green" title="E76">A6</font></span>: 
( <font color="Maroon" title="c5">H</font> is  <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a>  or <font color="Maroon" title="c5">H</font> is  <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a>  or <font color="Maroon" title="c5">H</font> is  <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a>  )
 <span class="kw">and </span><br/><a NAME="E5:83_1_1_2"/><span class="lab"><font color="Green" title="E77">A7</font></span>: 
<font color="Maroon" title="c3">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K6" title="MODELC_3:func.6">SuccNode2</a> (<font color="Maroon" title="c5">H</font>,<font color="Maroon" title="c4">N1</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#D8" target="_self" title="MODELC_3:def.8">Def8</a></span>;<br/><a NAME="E6:83_1_1_2"/>
 the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">N1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c5">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:83_1_1_2"><span class="lab"><font color="Green" title="E75">A5</font></span></a>, <a class="txt" href="#E5:83_1_1_2"><span class="lab"><font color="Green" title="E77">A7</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/><a NAME="E7:83_1_1_2"/><span class="kw">then </span>
( <font color="Maroon" title="c1">F</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c4">N1</font> or <font color="Maroon" title="c1">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="c5">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:83"><span class="lab"><font color="Green" title="E74">A3</font></span></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></span>;<br/><a NAME="E8:83_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c1">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">H</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:83"><span class="lab"><font color="Green" title="E73">A2</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E9:83_1_1_2"/>
<font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c4">N1</font>,<font color="Maroon" title="c1">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:83_1_1_2"><span class="lab"><font color="Green" title="E75">A5</font></span></a>, <a class="txt" href="#E4:83_1_1_2"><span class="lab"><font color="Green" title="E76">A6</font></span></a>, <a class="txt" href="#E5:83_1_1_2"><span class="lab"><font color="Green" title="E77">A7</font></span></a>, <a class="ref" href="modelc_3.html#D6" target="_self" title="MODELC_3:def.6">Def6</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E5:83"/>
<font color="Maroon" title="c3">N2</font> <a href="modelc_3.html#R1" title="MODELC_3:pred.1">is_succ_of</a> <font color="Maroon" title="c4">N1</font>,<font color="Maroon" title="c1">F</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
