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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#R3" title="MODELC_3:pred.3">is_succ2_of</a> <font color="Olive" title="b2">N1</font> holds <br/> <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Olive" title="b1">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Olive" title="b2">N1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</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#R3" title="MODELC_3:pred.3">is_succ2_of</a> <font color="Maroon" title="c3">N1</font> implies  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1 )</span><br/>





<b>set </b><font color="Maroon" title="c4">NN1</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font>;<br/>
<b>set </b><font color="Maroon" title="c5">NN2</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font>;<br/>
<b>assume </b><a NAME="E1:74"/>
<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">  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span><br/>

<b>then consider </b><font color="Maroon" title="c6">H</font> being   <a href="modelc_2.html#NM1" title="MODELC_2:NM.1">LTL-formula</a><b> such that </b><br/><a NAME="E3:74"/><i><font color="Green" title="E65">A1</font></i>: 
<font color="Maroon" title="c6">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="E4:74"/><i><font color="Green" title="E66">A101</font></i>: 
( <font color="Maroon" title="c6">H</font> is <a href="modelc_2.html#V5" title="MODELC_2:attr.5">disjunctive</a> or <font color="Maroon" title="c6">H</font> is <a href="modelc_2.html#V7" title="MODELC_2:attr.7">Until</a> or <font color="Maroon" title="c6">H</font> is <a href="modelc_2.html#V8" title="MODELC_2:attr.8">Release</a> )
 <b>and </b><br/><a NAME="E5:74"/><i><font color="Green" title="E67">A2</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="c6">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/>
<b>set </b><font color="Maroon" title="c7">New2</font> =  <a href="modelc_3.html#K20" title="MODELC_3:func.20">LTLNew2</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font>;<br/>
<b>set </b><font color="Maroon" title="c8">M1</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</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="c6">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<b>set </b><font color="Maroon" title="c9">M2</font> = <span class="p1">(<span class="default"><a href="modelc_3.html#K20" title="MODELC_3:func.20">LTLNew2</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c10">NN1</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c11">M1</font> = the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</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="c6">H</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span> ;<br/>
<b>reconsider </b><font color="Maroon" title="c12">M2</font> = <span class="p1">(<span class="default"><a href="modelc_3.html#K20" title="MODELC_3:func.20">LTLNew2</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> the <a href="modelc_3.html#U1" title="MODELC_3:sel.1">LTLold</a> of <font color="Maroon" title="c3">N1</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_3.html#K1" title="MODELC_3:func.1">Subformulae</a> <font color="Maroon" title="c1">v</font></span>)</span> ;<br/>
<a NAME="E9:74"/>
 <a href="modelc_3.html#K20" title="MODELC_3:func.20">LTLNew2</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="modelc_3.html#K3" title="MODELC_3:func.3">LTLNew2</a> <font color="Maroon" title="c6">H</font>
 
<b>by </b><i><a class="txt" href="#E3:74"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="modelc_3.html#D28" target="_self" title="MODELC_3:def.28">defLTLNew201</a></i>;<br/>
<a NAME="E10:74"/><b>then </b><i><font color="Green" title="E68">A3</font></i>: 
the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">M1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c12">M2</font>
 
<b>by </b><i><a class="txt" href="#E3:74"><i><font color="Green" title="E65">A1</font></i></a>, <a class="txt" href="#E4:74"><i><font color="Green" title="E66">A101</font></i></a>, <a class="txt" href="#E5:74"><i><font color="Green" title="E67">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="E11:74"/><i><font color="Green" title="E69">A4</font></i>: 
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">M1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c10">NN1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E3:74"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="modelc_3.html#T10" target="_self" title="MODELC_3:th.10">Thlen07</a></i>;<br/>
<a NAME="E12:74"/><i><font color="Green" title="E70">A5</font></i>: 
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K20" title="MODELC_3:func.20">LTLNew2</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
<b>by </b><i><a class="txt" href="#E3:74"><i><font color="Green" title="E65">A1</font></i></a>, <a class="txt" href="modelc_3.html#E75"><i><font color="Green" title="E62">lemlen06</font></i></a></i>;<br/>
<a NAME="E13:74"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c12">M2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K20" title="MODELC_3:func.20">LTLNew2</a> <font color="Maroon" title="c6">H</font>,<font color="Maroon" title="c1">v</font></span>)</span>
 
<b>by </b><i><a class="ref" href="modelc_3.html#T15" target="_self" title="MODELC_3:th.15">Thlen12</a>, <a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></i>;<br/>
<a NAME="E14:74"/><b>then </b>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c12">M2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 
<b>by </b><i><a class="txt" href="#E12:74"><i><font color="Green" title="E70">A5</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/>
<a NAME="E15:74"/><b>then </b><i><font color="Green" title="E71">A6</font></i>: 
<span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">M1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c12">M2</font></span>)</span> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">M1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c6">H</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1</span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/>
<a NAME="E16:74"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">M1</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c12">M2</font></span>)</span>
 
<b>by </b><i><a class="txt" href="#E10:74"><i><font color="Green" title="E68">A3</font></i></a>, <a class="ref" href="modelc_3.html#T18" target="_self" title="MODELC_3:th.18">Thlen13</a></i>;<br/>
<b>hence </b><a NAME="E17:74"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c2">N2</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> the <a href="modelc_3.html#U2" title="MODELC_3:sel.2">LTLnew</a> of <font color="Maroon" title="c3">N1</font></span>)</span> <a href="real_1.html#K9" title="REAL_1:func.9">-</a> 1
 <b>by </b><i><a class="txt" href="#E15:74"><i><font color="Green" title="E71">A6</font></i></a>, <a class="txt" href="#E11:74"><i><font color="Green" title="E69">A4</font></i></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>; <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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