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<b>let </b><font color="Maroon" title="c1">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">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="c1">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> holds <br/>( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b2">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Olive" title="b1">N2</font> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Olive" title="b2">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Olive" title="b1">N2</font> )</span><br/><b>let </b><font color="Maroon" title="c2">N2</font>, <font color="Maroon" title="c3">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="c1">v</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">N2</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c3">N1</font> implies ( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N2</font> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N2</font> ) )</span><br/>





<b>assume </b><a NAME="E1:80"/><i><font color="Green" title="E69">A1</font></i>: 
<font color="Maroon" title="c2">N2</font> <a href="modelc_3.html#R4" title="MODELC_3:pred.4">is_succ_of</a> <font color="Maroon" title="c3">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N2</font> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N2</font> )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="80_1"><b>now </b></a><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="80_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:80_1_1"/>
( <font color="Maroon" title="c2">N2</font> <a href="modelc_3.html#R2" title="MODELC_3:pred.2">is_succ1_of</a> <font color="Maroon" title="c3">N1</font> or <font color="Maroon" title="c2">N2</font> <a href="modelc_3.html#R3" title="MODELC_3:pred.3">is_succ2_of</a> <font color="Maroon" title="c3">N1</font> )
 </span><b>by </b><i><a class="txt" href="#E1:80"><i><font color="Green" title="E69">A1</font></i></a>, <a class="ref" href="modelc_3.html#D9" target="_self" title="MODELC_3:def.9">Def210</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="80_1_1_1"><b>suppose </b></a><a NAME="E1:80_1_1_1"/>
<font color="Maroon" title="c2">N2</font> <a href="modelc_3.html#R2" title="MODELC_3:pred.2">is_succ1_of</a> <font color="Maroon" title="c3">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N2</font> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N2</font> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E3:80_1_1_1"/><i><font color="Green" title="E70">B1</font></i>: 
<font color="Maroon" title="c4">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">N1</font>
 <b>and </b><br/><a NAME="E4:80_1_1_1"/><i><font color="Green" title="E71">B2</font></i>: 
<font color="Maroon" title="c2">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="c4">H</font>,<font color="Maroon" title="c3">N1</font>
 <b>by </b><i><a class="ref" href="modelc_3.html#D7" target="_self" title="MODELC_3:def.7">Def208</a></i>;<br/><a NAME="E5:80_1_1_1"/>
( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">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="c3">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="c4">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K4" title="MODELC_3:func.4">LTLNext</a> <font color="Maroon" title="c4">H</font></span>)</span> )
 <b>by </b><i><a class="txt" href="#E3:80_1_1_1"><i><font color="Green" title="E70">B1</font></i></a>, <a class="txt" href="#E4:80_1_1_1"><i><font color="Green" title="E71">B2</font></i></a>, <a class="ref" href="modelc_3.html#D4" target="_self" title="MODELC_3:def.4">Def206</a></i>;<br/><b>hence </b><a NAME="E6:80_1_1_1"/>
( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N2</font> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N2</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</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="80_1_1_2"><b>suppose </b></a><a NAME="E1:80_1_1_2"/>
<font color="Maroon" title="c2">N2</font> <a href="modelc_3.html#R3" title="MODELC_3:pred.3">is_succ2_of</a> <font color="Maroon" title="c3">N1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N2</font> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N2</font> )</span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c4">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E3:80_1_1_2"/><i><font color="Green" title="E70">B1</font></i>: 
<font color="Maroon" title="c4">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">N1</font>
 <b>and </b><br/><a NAME="E4:80_1_1_2"/><i><font color="Green" title="E71">B2</font></i>: 
( <font color="Maroon" title="c4">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c4">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c4">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> )
 <b>and </b><br/><a NAME="E5:80_1_1_2"/><i><font color="Green" title="E72">B3</font></i>: 
<font color="Maroon" title="c2">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="c4">H</font>,<font color="Maroon" title="c3">N1</font>
 <b>by </b><i><a class="ref" href="modelc_3.html#D8" target="_self" title="MODELC_3:def.8">Def209</a></i>;<br/><a NAME="E6:80_1_1_2"/>
( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">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="c3">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="c4">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N1</font> )
 <b>by </b><i><a class="txt" href="#E3:80_1_1_2"><i><font color="Green" title="E70">B1</font></i></a>, <a class="txt" href="#E4:80_1_1_2"><i><font color="Green" title="E71">B2</font></i></a>, <a class="txt" href="#E5:80_1_1_2"><i><font color="Green" title="E72">B3</font></i></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def207</a></i>;<br/><b>hence </b><a NAME="E7:80_1_1_2"/>
( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N2</font> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N2</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</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="E3:80"/>
( the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c2">N2</font> &amp; the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c3">N1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="modelc_3.html#U3" title="MODELC_3:sel.3">LTLnext</a> of <font color="Maroon" title="c2">N2</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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