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<span class="kw">let </span><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:()"><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="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/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>





<span class="kw">set </span><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/>
<span class="kw">set </span><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/>
<span class="kw">assume </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">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="E3:74"/><span class="lab"><font color="Green" title="E65">A1</font></span>: 
<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>
 <span class="kw">and </span><br/><a NAME="E4:74"/>
( <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>  )
 <span class="kw">and </span><br/><a NAME="E5:74"/><span class="lab"><font color="Green" title="E66">A2</font></span>: 
<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>)
 <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/>
<span class="kw">set </span><font color="Maroon" title="c7">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/>
<span class="kw">set </span><font color="Maroon" title="c8">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/>
<span class="kw">set </span><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/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">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/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">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="E8:74"/>
 <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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="modelc_3.html#D28" target="_self" title="MODELC_3:def.28">Def28</a></span>;<br/>
<a NAME="E9:74"/><span class="kw">then </span>
 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="c10">M1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c11">M2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="txt" href="#E5:74"><span class="lab"><font color="Green" title="E66">A2</font></span></a>, <a class="ref" href="modelc_3.html#D5" target="_self" title="MODELC_3:def.5">Def5</a></span>;<br/>
<a NAME="E10:74"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A3</font></span>: 
 <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="c10">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="c11">M2</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#T18" target="_self" title="MODELC_3:th.18">Th18</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">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/>
<a NAME="E12:74"/><span class="lab"><font color="Green" title="E68">A4</font></span>: 
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_3.html#T15" target="_self" title="MODELC_3:th.15">Th15</a>, <a class="ref" href="xboole_1.html#T36" title="XBOOLE_1:th.36">XBOOLE_1:36</a></span>;<br/>
<a NAME="E13:74"/>
 <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
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="txt" href="modelc_3.html#E75"><span class="lab"><font color="Green" title="E62">Lm29</font></span></a></span>;<br/>
<a NAME="E14:74"/><span class="kw">then </span>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c11">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
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:74"><span class="lab"><font color="Green" title="E68">A4</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></span>;<br/>
<a NAME="E15:74"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A5</font></span>: 
<span class="p1">(<span class="default"><a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c10">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="c11">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="c10">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T6" title="XREAL_1:th.6">XREAL_1:6</a></span>;<br/>
<a NAME="E16:74"/>
 <a href="modelc_3.html#K18" title="MODELC_3:func.18">len</a> <font color="Maroon" title="c10">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="c12">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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E65">A1</font></span></a>, <a class="ref" href="modelc_3.html#T10" target="_self" title="MODELC_3:th.10">Th10</a></span>;<br/>
<span class="kw">hence </span><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
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:74"><span class="lab"><font color="Green" title="E69">A5</font></span></a>, <a class="txt" href="#E10:74"><span class="lab"><font color="Green" title="E67">A3</font></span></a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</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/>


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